Exhibit 10.1

May 9, 2013

By Hand Delivery

Vicente Trelles

5760 Daniel Road, Apt 7311

Plano, Texas 75024

Dear Vicente:

As we have previously discussed, the decision has been reached to not renew your employment agreement (“Employment Agreement”) with Orthofix, Inc. (the “Company”) at the end of its current term which expires on July 1, 2013. Because we value your services to the Company, however, we have prepared a severance package to assist you through this transition. Provided that you accept it, this letter confirms the agreement (“Agreement”) between you and the Company concerning your severance arrangements, as follows:

1. Separation Date; Post-Separation Obligations.

(a) Rather than requiring you to continue working until July 1, 2013, you and the Company have agreed that your last day in the office and your official employment with the Company will end as of May 10, 2013 (the “Separation Date”). On the Separation Date, you will tender written resignations to the Company with respect to all officer and director positions you hold at that time with the Company and any member of the Parent Group as that term is defined in the Employment Agreement.

(b) From the Separation Date and continuing through June 30, 2013, you agree to remain available to the Company, when and as requested, to assist in the transition of your responsibilities.

(c) You agree to participate in an exit interview with the Company, at a time mutually agreed-upon but within two weeks of the Separation Date, and to respond fully and accurately to the questions posed by the Company.

2. Final Wages, Vacation Pay and Insurance Benefits. Within ten (10) days of the Separation Date, you will receive pay, at your final base salary ($410,040 per annum), for all work performed for the Company from the end of the last payroll period through the Separation Date, to the extent not previously paid. In addition, the Company will pay you at that time for all hours of vacation time you have earned, but not used, as of the Separation Date, determined in accordance with Company policy and as reflected on Company records. These amounts will be paid to you whether or not you accept this Agreement.

3. Severance Benefits. In consideration of your acceptance of this Agreement and subject to your fully meeting your obligations under it, the Company will provide you the following severance benefits:

(a) A one-time lump sum severance payment in an amount equal to (i) $466,724.40 plus (ii) $12,500 to be used by you for outplacement services less (iii) the Reimbursed Legal Expenses (as defined below) (collectively, the “Severance Payment”). The Severance Payment shall be paid on the 60th day following your Separation Date, provided that prior to such time you have signed the release attached hereto as Exhibit A (the “Release”) and the applicable revocation period for such Release has expired. In the event that the Release is not signed and effective (with the applicable revocation period having expired) by such 60th day following your Separation Date, the Severance Payment shall be forfeited and the Company shall have no obligation to pay them to you at any time in the future. The parties agree that included in the Severance Payment are all amounts payable to you under the Company’s annual incentive program, including any pro-rated amounts payable with respect to the 2013 fiscal year, and that you will not receive any further bonus under the Company’s annual incentive program other than amounts included in the Severance Payment.

(b) Provided you are eligible and elect in a timely manner to continue your participation and that of your eligible dependents in the Company’s medical and dental benefit plans under the Consolidated Omnibus Budget Reconciliation Act of 1985 (“COBRA”), then, for the lesser of 18 months after the Separation Date or until you secure coverage from new employment, you shall receive a monthly cash payment from the Company equal to the cost of coverage under the medical and dental benefit plans in which you were participating on the Separation Date, at the level at which you were participating (e.g. single or family coverage), less the amount of your contribution for such coverage. Such payments shall be subject to all applicable taxes and withholding.

(c) Your separation of employment shall be treated as a termination without “cause” pursuant to: (i) Section 5(b) of your Inducement Stock Option Agreement dated April 1, 2011 with Orthofix International N.V. (“Parent”); (ii) Section 6(b) of your Non-Qualified Stock Option Agreement dated February 15, 2012 with Parent; (iii) Section 6(a) of your Non-Qualified Stock Option Agreement dated June 25, 2012 with Parent; and (iv) Section 5(a) of your Restricted Stock Grant Agreement dated July 31, 2012 with Parent.

4. Tax Withholding. All payments made by the Company under this Agreement will be reduced by all taxes and other amounts that the Company is required to withhold under applicable law and by all other deductions authorized by you.

5. Acknowledgement of Full Payment and Status of Benefits. You acknowledge and agree that the payments provided under paragraphs 2 and 3 of this Agreement are in full and complete satisfaction of any and all compensation or benefits due to you from the Company, whether for services provided or otherwise, through the Separation Date and that, except as expressly provided under this Agreement, no further compensation or benefits of any kind are owed or will be paid to you. You will not continue to earn vacation or other paid time off after the Separation Date and, except as expressly provided in paragraph 3(b) of this Agreement, your participation in all employee benefit plans and programs of the Company will end as of the Separation Date, in accordance with the terms of those plans and programs.

6. Survival. You acknowledge and agree that, pursuant Section 1.3 of the Employment Agreement, Articles VI and VII of the Employment Agreement survive the termination or expiration of the Employment Agreement for any reason and that you will continue to comply with each of their provisions. Notwithstanding the foregoing, the parties hereby agree that the twelve-month post-employment periods referenced in Sections 6.1 and 6.2 of the Employment Agreement are hereby amended to become six-month post-employment periods under such respective sections.

7. Release of Claims.

(a) The Company’s obligation to pay or provide any benefits to you under this Agreement is expressly subject to the requirement that, no later than the 60th day following your Separation Date, you have both previously executed the Release and the revocation period provided for the Release shall have expired without your having breached or revoked the Release. In the event that you do not timely sign the Release as contemplated by the prior sentence, or sign and later revoke the Release, all of the Company’s obligations to make payments and provide benefits under this Agreement will terminate in full, and you understand and agree that you will not be entitled to any severance benefits in connection with the non-renewal of your Employment Agreement.

(b) The Company wants to be certain that this Agreement will resolve any and all concerns that you might have and therefore requests that you carefully consider the terms of this Agreement, including the Release. This Agreement, which includes the Release, creates legally-binding obligations and the Company therefore advises you to consult an attorney before you sign this Agreement.

8. Miscellaneous.

(a) Following the Separation Date, you will no longer have access to our offices. If you need to come to the office, please contact me in advance of coming so that we can discuss your request and make any appropriate arrangements.

(b) This letter contains the entire agreement between you and the Company and supersedes all prior and contemporaneous agreements, communications and understandings, whether written or oral, with respect to your employment and its termination and all related matters, excluding only those provisions of the Employment Agreement which, by their terms, are intended to continue in full force and effect.

(c) This Agreement may not be modified or amended, and no breach shall be deemed to be waived, unless agreed to in writing by you and an expressly authorized representative of the Company. The captions and headings in this Agreement are for convenience only and in no way define or describe the scope or content of any provision of this Agreement.

(d) In signing this Agreement, you give the Company assurance that you have had a full and reasonable opportunity to consider its terms and to consult with an attorney if you wished to do so; that you have read and understood all of those terms; that your acceptance of this Agreement is freely and voluntarily given; and that, in signing this Agreement, you have not relied on any promises or representations, express or implied, that are not set forth expressly in this Agreement.

(e) The Company shall pay on your behalf outside legal expenses (subject to the receipt of a customary invoice from your counsel) incurred by you in connection with the negotiation of this Agreement in an amount up to $10,000 (the “Reimbursed Legal Expenses”)

If the terms of this Agreement are acceptable to you, please sign, date and return it to me, together with the Release, no later than twenty one (21) days from the date you receive it. You may revoke this Agreement, and the Release, at any time during the seven-day period immediately following the date of your signing by notifying me in writing of your revocation within that period. If you do not so revoke this Agreement and the Release, then, on the eighth calendar day following the date of your signing (the “Effective Date”), this Agreement and the Release shall take effect as legally-binding agreements between you and the Company on the basis set forth above. The enclosed copy of this letter, which you should also sign and date, is for your records.

Formalities aside, I want to take this opportunity to thank you for all of your efforts on behalf of the Company and to wish you well in your future endeavors.

Sincerely,

/s/ Tonjia Oglesby

Tonjia Oglesby

Vice President, Human Resources

EXHIBIT A

RELEASE

In exchange for the consideration set forth in the Agreement to which this Release is attached, by and among Orthofix Inc. (the “Company”) and myself, the respective terms of which are incorporated herein by reference, I, Vicente Trelles, am entering into this Release (this “Release”) for good and valuable consideration to which I am not otherwise entitled, and agree as follows:

1. GENERAL RELEASE.

(a) On behalf of myself, my heirs, executors, successors and assigns, I irrevocably and unconditionally release, waive and forever discharge the Company, its members, divisions, subsidiaries, affiliates and related companies, including the Company Group (as defined below), or any member of the Company Group, and their present and former agents, employees, officers, directors, attorneys, stockholders, plan fiduciaries, successors and assigns (collectively, the “Releasees”), from any and all claims, demands, actions, causes of action, costs, fees and all liability whatsoever, whether known or unknown, fixed or contingent, suspected or unsuspected (collectively, “Claims”), which I had, have, or may have against Releasees relating to or arising out of my employment by or separation from the Company and its direct and indirect subsidiaries and parents, including, without limitation, Orthofix International N.V. (collectively, the “Company Group”), up to and including the date of execution of this Release, other than my right to receive the severance payments and other benefits and consideration described in the Agreement. This Release includes, without limitation: (i) claims at law or equity or sounding in contract (express or implied) or tort; (ii) claims arising under any federal, state or local laws of any jurisdiction that prohibit age, sex, race, national origin, color, disability, religion, veteran or military status, sexual orientation or any other form of discrimination, harassment or retaliation (including, without limitation, the Civil Rights Act of 1866, the Age Discrimination in Employment Act, the Older Workers Benefit Protection Act, the Americans with Disabilities Act, Title VII of the 1964 Civil Rights Act, the Civil Rights Act of 1991, the Rehabilitation Act, the Family and Medical Leave Act, the Sarbanes-Oxley Act, the Employee Polygraph Protection Act, the Uniformed Services Employment and Reemployment Rights Act of 1994, the Unruh Civil Rights Act, or any other federal, state or local laws, regulations and ordinances governing discrimination, harassment or retaliation in employment; and the right to bring demands, complaints, causes of action, and claims under any other federal, state, local or common law, statute, regulation or decision); (iii) claims arising under the Employee Retirement Income Security Act; or (iv) any other statutory or common law claims related to my employment with the Company or my separation from the Company. I further covenant not to sue any of the Releasees with respect to any matters released hereby.

(b) This release does not include a release or waiver of any rights or claims I have, or might subsequently have in my capacity as a stockholder of Orthofix International N.V. I am also not waiving, and nothing in this Release is intended to waive, any right to coverage under any directors and officers insurance coverage, if any, provided by the Company, the Company Group, or any member of the Company Group, or any right to indemnification or

expense advancement under any indemnification agreement, or any applicable Company Group articles of incorporation, bylaws or similar organizational document, if any, in each case, to which I might be entitled. I am also not waiving, and nothing in this Release is intended to waive any claims I may have for unemployment insurance or workers’ compensation benefits, state disability compensation, claims for any vested benefits under any Company-sponsored benefit plan, or any claims that, as a matter of law, may not be released by private agreement. I am also not waiving, and nothing in this Release is intended to waive, any claims relating to the validity or enforceability of this Release; or any non-waivable right to file a charge with the United States Equal Employment Opportunity Commission (the “EEOC”) or the National Labor Relations Board (“NLRB”); provided, however, that I shall not be entitled to recover any monetary damages or to non-monetary relief if the EEOC or NLRB were to pursue any claims relating to my employment with the Company.

EXCEPT AS OUTLINED ABOVE, THIS MEANS THAT, BY SIGNING THIS RELEASE, I WILL WAIVE ANY RIGHT I MAY HAVE HAD TO PURSUE OR BRING A LAWSUIT OR MAKE ANY LEGAL CLAIM AGAINST THE COMPANY OR THE RELEASEES THAT IN ANY WAY ARISES FROM OR RELATES TO MY EMPLOYMENT OR THE TERMINATION OF THAT EMPLOYMENT, UP TO AND INCLUDING THE DATE OF THE EXECUTION OF THIS RELEASE.

(c) I acknowledge that different or additional facts may be discovered in addition to what I now know or believe to be true with respect to the matters herein released, and I agree that this Release shall be and remain in effect in all respects as a complete and final release of the matters released, notwithstanding any such different or additional facts. I represent and warrant that I have not previously filed or joined in any claims against the Company or any of the Releasees, that I have not given or sold any portion of any claims released herein to anyone else, and that I will indemnify and hold harmless the Releasees from all liabilities, claims, demands, costs, expenses and/or attorneys’ fees incurred as a result of any such assignment or transfer.

(d) I acknowledge that I have been given an opportunity of twenty-one (21) days to consider this Release, but I may voluntarily waive that period by signing it earlier, and I acknowledge that I am being advised herein to consult with legal counsel of my own choosing prior to executing this Release. I understand that for a period ending at the end of the seventh calendar day following my execution of this Release (“Revocation Period”), I shall have the right to revoke this Release by delivering a written notice of revocation to Jeffrey Schumm, Orthofix Inc., Senior Vice President and General Counsel, Orthofix Inc., 3451 Plano Parkway, Lewisville, TX 75056 no later than the end of the seventh calendar day after I sign this Release. I understand and agree that this Release will not be effective and enforceable until after the Revocation Period expires without revocation, and if I elect to exercise this revocation right, this Release shall be voided in its entirety, and the Company shall be relieved of all obligations under this Release and all obligations under the Agreement as provided therein. This Release shall be effective on the eighth calendar day after it is executed by me (“Effective Date”) provided it has not been previously revoked as provided herein.

2. I agree not to disclose, publish or use any confidential information of the Company Group, except as the Company directs or authorizes unless required by law to do so. I also agree that I will take all reasonable measures to protect the secrecy of and avoid disclosure and unauthorized use of confidential information of the Company Group, and I will immediately notify the Company in the event of any unauthorized use or disclosure of the Company Group’s confidential information of which I become aware. I agree that the obligations set forth in this paragraph do not supersede, but are in addition to, any previous confidentiality obligations agreed to by me and any member of the Company Group. The confidentiality provisions set forth in this Release are contractual and their terms are material to this Release. In any proceeding brought to enforce or seek damages for the alleged breach of the confidentiality provisions of this Release, the party successfully prosecuting or defending such action shall be entitled to recover from the opposing party its reasonable expenses, including attorneys’ fees.

3. I agree to hold harmless the Releasees, at my sole cost and expense, from and against any claims arising from my breach of this Release (including breaches of my post separation obligations under the Agreement).

4. I agree that I have not made and shall not make, publicly or privately, any critical or negative comments to the media or any significant critical or negative comments to any other person (including future or prospective employees) regarding any of the Releasees. The Company and Parent further agree that they shall not make, and shall commercially reasonable efforts to prevent any of their respective officers or directors from making, any critical or negative comments to the media or other persons about me, provided that the foregoing shall in no way limit Parent’s right to make any public statements or disclosures it believes, after consultation with counsel, are required or appropriate pursuant to applicable federal securities laws.

5. I understand it is my choice whether or not to enter into this Release and that my decision to do so is voluntary and is made knowingly.

6. I represent and acknowledge that in executing this Release, I do not rely, and have not relied, on any communications, statements, inducements or representations, oral or written, by any of the Releasees, except as expressly contained in this Release.

7. I also represent and warrant that, on or before my last date of employment, I will have delivered to the Company (a) all documents and materials containing confidential information (including without limitation any “soft” copies or computerized or electronic versions thereof) or otherwise containing information relating to the business and affairs of any member of the Company Group (whether or not confidential), and (b) all other documents, materials and other property belonging to any member of the Company Group that are or were in my possession or under my control.

8. The Company and I agree that this Release shall be binding on us and our heirs, administrators, representatives, executors, successors and assigns, and shall inure to the benefit of our heirs, administrators, representatives, executors, successors and assigns.

9. This Release shall be interpreted under and governed by the laws of the State of Texas. The Company and I agree that the language of this Release shall in all cases be construed as a whole, according to its fair meaning, and not strictly for or against either party.

10. The Company and I agree that should that any provision of this Release be determined to be illegal or invalid, the validity of the remaining provisions will not be affected and any illegal or invalid provision will be deemed not to be a part of this Release.

11. The Company and I agree that this Release may be executed in any number of counterparts, each of which shall be deemed an original, but all of which together shall be deemed one and the same instrument.

Please read carefully as this document includes a General Release of claims.

As evidenced by my signature below, I certify that I have read the above Release and agree to its terms.