Exhibit 4.1

Form of April 2012 Extension Warrant

THIS SECURITY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT (AS DEFINED HEREIN), OR UNDER ANY STATE SECURITIES LAWS, IN RELIANCE UPON EXEMPTIONS FROM REGISTRATION FOR NON-PUBLIC OFFERINGS. THIS SECURITY MAY ONLY BE SOLD OR OTHERWISE TRANSFERRED TO A “PERMITTED TRANSFEREE” (AS DEFINED HEREIN) OR PURSUANT TO AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT AND APPLICABLE STATE SECURITIES LAWS OR IN A TRANSACTION EXEMPT FROM THE SECURITIES ACT AND ANY APPLICABLE STATE SECURITIES LAWS.

STEREOTAXIS, INC.

COMMON STOCK PURCHASE WARRANT

TO PURCHASE SHARES OF

COMMON STOCK, $0.001 PAR VALUE PER SHARE

This is to certify that, FOR VALUE RECEIVED,                     (“Warrantholder”), is entitled to purchase, subject to the provisions of this Common Stock Purchase Warrant (“Warrant”), from Stereotaxis, Inc., a corporation organized under the laws of Delaware (“Company”), at any time and from time to time on or after the Issue Date above, but not later than 5:00 P.M., St. Louis, Missouri time, on March 30, 2017 (the “Expiration Date”), [            ]¹ shares (“Warrant Shares”) of Common Stock, $0.001 par value (“Common Stock”), of the Company, at an exercise price per share equal to $0.6602 (the exercise price in effect from time to time hereafter being herein called the “Warrant Price”). The number of Warrant Shares purchasable upon exercise of this Warrant and the Warrant Price shall be subject to adjustment from time to time as described herein.

This Warrant has been issued pursuant to the terms of the Note and Warrant Purchase Agreement, dated February 21, 2008, amended by the First Amendment to Note and Warrant Purchase Agreement, made effective as of December 29, 2008, the Second Amendment to Note and Warrant Purchase Agreement, dated as of October 9, 2009, the Third Amendment to Note and Warrant Purchase Agreement, dated as of November 10, 2010, and by the Fourth Amendment to Note and Warrant Purchase Agreement, dated as of March 30, 2012 (as amended, the “Purchase Agreement”) by and among the Company, the Warrantholder and the other lenders set forth therein. Capitalized terms used herein and not defined shall have the meaning specified in the Purchase Agreement.

1. Registration. The Company shall maintain books for the transfer and registration of the Warrant. Upon the initial issuance of the Warrant, the Company shall issue and register the Warrant in the name of the Warrantholder.

2. Transfers. As provided herein, this Warrant may be transferred only pursuant to a registration statement filed under the Securities Act of 1933, as amended (the “Securities Act”), or an exemption from registration thereunder. Subject to such restrictions, the Company shall transfer this Warrant from time to time, upon the books to be maintained by the Company for that purpose, upon surrender hereof for transfer properly endorsed or accompanied by appropriate instructions for transfer upon any such transfer, and a new Warrant shall be issued to the transferee and the surrendered Warrant shall be canceled by the Company. References to Warrantholder or holder shall include any such transferee.

3. Exercise of Warrant. The Warrantholder may exercise this Warrant to purchase the Warrant Shares, in whole or in part, at any time and from time to time on and after the Issue Date and before the Expiration Date upon surrender of the Warrant, together with delivery of the duly executed Warrant exercise form attached hereto (the “Exercise Agreement”) (which may be by fax or portable document format (pdf) delivered by email), to the Company during normal business hours on any business day at the Company’s principal executive offices (or such other office or agency of the Company as it may designate by notice to the holder hereof), and upon payment to the Company in cash, by certified or official bank check or by wire transfer for the account of the Company of the Warrant Price for the Warrant Shares specified in the Exercise Agreement. The Warrant Shares so purchased shall be deemed to be issued to the holder hereof or such holder’s designee, as the record owner of such shares, as of the close of business on the date on which the completed Exercise Agreement shall have been delivered to the Company (or such later date as may be specified in the Exercise Agreement). Certificates for the Warrant Shares so purchased, representing the aggregate number of shares specified in the Exercise Agreement, shall be delivered to the holder hereof within a reasonable time, not exceeding five (5) business days, after this Warrant shall have been so exercised. The certificates so delivered shall be in such denominations as may be requested by the holder hereof and shall be registered in the name of such holder or such other name as shall be designated by such holder. If this Warrant shall have been exercised only in part, then, unless this Warrant has expired, the Company shall, at its expense, at the time of delivery of such certificates, deliver to the holder a new Warrant representing the number of shares with respect to which this Warrant shall not then have been exercised.

4. Cashless Exercise. (a) The Warrantholder may, at its election exercised in its sole discretion, exercise this Warrant and, in lieu of making the cash payment otherwise contemplated to be made to the Company upon such exercise in payment of the Warrant Price for the Warrant Shares specified in the Exercise Agreement, elect instead to receive upon such exercise the “Net Number” of shares of Common Stock determined according to the following formula (a “Cashless Exercise”):

Net Number = (A x B) - (A x C)

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B

For purposes of the foregoing formula:

A = the total number of shares with respect to which this Warrant is then being exercised.

B = the Closing Price of the Common Stock on NASDAQ on the Trading Day immediately preceding the date of the Exercise Notice.

C = the Warrant Price then in effect for the applicable Warrant Shares at the time of such exercise.

(b) Certain Definitions.

“Trading Day” shall mean a day on which the principal national securities exchange on which the Common Stock is listed or admitted to trading is open for business.

“Closing Price” with respect to Common Stock on any day means the reported last sales price regular way on The NASDAQ Global Select Market (“NASDAQ”), or, if no such reported sale occurs on such day, the average of the closing bid and asked prices regular way on such day, in each case as reported in the principal consolidated transaction reporting system with respect to securities listed on the principal national securities exchange on which such class of security is listed or admitted to trading as reported by NASDAQ or any comparable system then in use or, if not so reported, as reported by any New York Stock Exchange member firm reasonably selected by the Company for such purpose.

5. Compliance with the Securities Act. Neither this Warrant nor the Common Stock issued upon exercise hereof nor any other security issued or issuable upon exercise of this Warrant may be offered or sold except as provided in this Warrant and in conformity with the Securities Act, and then only against receipt of an agreement of such person to whom such offer of sale is made to comply with the provisions of this Section 5 with respect to any resale or other disposition of such security. The Company may cause the legend set forth on the first page of this Warrant to be set forth on each Warrant or similar legend on the Warrant Shares or any other security issued or issuable upon exercise of this Warrant until the Warrant Shares have been registered for resale, unless counsel for the Company is of the opinion as to any such security that such legend is unnecessary.

6. Payment of Taxes. The Company will pay any documentary stamp taxes attributable to the initial issuance of Warrant Shares issuable upon the exercise of the Warrant; provided, however, that the Company shall not be required to pay any tax or taxes which may be payable in respect of any transfer involved in the issuance or delivery of any certificates for Warrant Shares in a name other than that of the registered holder of this Warrant in respect of which such shares are issued. The holder shall be responsible for income taxes due under federal or state law, if any such tax is due.

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7. Mutilated or Missing Warrants. In case this Warrant shall be mutilated, lost, stolen, or destroyed, the Company shall issue in exchange and substitution of and upon cancellation of the mutilated Warrant, or in lieu of and substitution for the Warrant lost, stolen or destroyed, a new Warrant of like tenor and for the purchase of a like number of Warrant Shares, but only upon receipt of evidence reasonably satisfactory to the Company of such loss, theft or destruction of the Warrant, and with respect to a lost, stolen or destroyed Warrant, reasonable indemnity or bond with respect thereto, if reasonably requested by the Company.

8. Insufficient Authorized Shares. If at any time while this Warrant remains outstanding the Company does not have a sufficient number of authorized and unreserved shares of Common Stock to satisfy its obligation to reserve for issuance upon exercise of this Warrant at least a number of shares of Common Stock equal to (the “Required Reserve Amount”) the number of shares of Common Stock as shall from time to time be necessary to effect the exercise of all of this Warrant then outstanding (an “Authorized Share Failure”), then the Company shall, within 90 days after the occurrence of such Authorized Share Failure take action to increase the Company’s authorized and unissued shares of Common Stock to an amount sufficient to allow the Company to reserve the Required Reserve Amount for this Warrant then outstanding. The Company shall not be in breach of its obligation to reserve the Required Reserve Amount during such period so long as it is taking good faith efforts to satisfy its obligations under this covenant.

9. Warrant Price. The Warrant Price, subject to adjustment as provided in Section 10 hereof, shall, if payment is made in cash or by certified check, be payable in lawful money of the United States of America.

10. Adjustment of Warrant Exercise Price and Number of Shares. If the Company at any time after the date of issuance of this Warrant subdivides (by any stock split, stock dividend, recapitalization or otherwise) one or more classes of its outstanding shares of Common Stock into a greater number of shares, the Warrant Price in effect immediately prior to such subdivision will be proportionately reduced and the number of shares of Common Stock obtainable upon exercise of this Warrant will be proportionately increased. If the Company at any time after the date of issuance of this Warrant combines (by combination, reverse stock split or otherwise) one or more classes of its outstanding shares of Common Stock into a smaller number of shares, the Warrant Price in effect immediately prior to such combination will be proportionately increased and the number of shares of Common Stock obtainable upon exercise of this Warrant will be proportionately decreased. Any adjustment under this Section 10 shall become effective at the close of business on the date the subdivision or combination becomes effective.

11. Replacement Warrants. The Company agrees that after any request from time to time of the Warrantholder and within ten (10) business days upon the Company’s receipt of this Warrant, the Company shall deliver to such holder a new Warrant in substitution of this Warrant which is identical in all respects except that the then Warrant Price shall be appropriately specified in the Warrant, and the Warrant shall specify the fixed number of Warrant Shares into which this Warrant is then exercisable. Such changes are intended not as amendments to the Warrant but only as clarification of the adjustment in the preceding Section for convenience purposes, and such adjustments shall not affect any provisions concerning adjustments to the Warrant Price or number of Warrant Shares contained herein.

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12. Fractional Interest. The Company shall not be required to issue fractions of Warrant Shares upon the exercise of the Warrant. If any fraction of a Warrant Share would, except for the provisions of this Section, be issuable upon the exercise of the Warrant (or specified portions thereof), the Company shall round such calculation to the nearest whole number and disregard the fraction.

13. Benefits. Nothing in this Warrant shall be construed to give any person, firm or corporation (other than the Company and the Warrantholder) any legal or equitable right, remedy or claim, it being agreed that this Warrant shall be for the sole and exclusive benefit of the Company and the Warrantholder.

14. Notices to Warrantholder. Upon the happening of any event requiring an adjustment of the Warrant Price, the Company shall forthwith give written notice thereof to the Warrantholder at the address appearing in the records of the Company, stating the adjusted Warrant Price and the adjusted number of Warrant Shares resulting from such event and setting forth in reasonable detail the method of calculation and the facts upon which such calculation is based. In the event of a dispute with respect to any such calculation, the certificate of the Company’s independent certified public accountants shall be conclusive evidence of the correctness of any computation made, absent manifest error. Failure to give such notice to the Warrantholder or any defect therein shall not affect the legality or validity of the subject adjustment.

15. Identity of Transfer Agent. The Transfer Agent for the Common Stock is Broadridge. Forthwith upon the appointment of any subsequent transfer agent for the Common Stock or other shares of the Company’s capital stock issuable upon the exercise of the rights of purchase represented by the Warrant, the Company will fax to the Warrantholder a statement setting forth the name and address of such transfer agent.

16. Notices. Any notice pursuant hereto to be given or made by the Warrantholder to or on the Company shall be sufficiently given or made if delivered personally or by facsimile or if sent by an internationally recognized courier, addressed as follows:

Stereotaxis, Inc.

4320 Forest Park Avenue, Suite 100

St. Louis, Missouri 63108

Fax: (314) 678-6110

Attention: Chief Financial Officer

or such other address as the Company may specify in writing by notice to the Warrantholder complying as to delivery with the terms of this Section 16.

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Any notice pursuant hereto to be given or made by the Company to or on the Warrantholder shall be sufficiently given or made if personally delivered, if sent by facsimile or if sent by an internationally recognized courier service by overnight or two-day service, to the address set forth on the books of the Company or, as to each of the Company and the Warrantholder, at such other address as shall be designated by such party by written notice to the other party complying as to delivery with the terms of this Section 16.

All such notices, requests, demands, directions and other communications shall, when sent by courier, be effective two (2) days after delivery to such courier as provided and addressed as aforesaid. All faxes shall be effective upon receipt.

17. Registration Rights. The holder of this Warrant is entitled to the benefit of certain registration rights in respect of the Warrant Shares as provided in the Purchase Agreement.

18. Successors. Subject to the restrictions on transfer described in Section 21 below, all the covenants and provisions hereof by or for the benefit of the Warrantholder shall bind and inure to the benefit of its respective successors and assigns hereunder.

19. Governing Law. This Warrant shall be deemed to be a contract made under the laws of the State of Delaware, without giving effect to its conflict of law principles, and for all purposes shall be construed in accordance with the laws of said State.

20. Absolute Obligation to Issue Warrant Shares. The Company’s obligations to issue and deliver Warrant Shares in accordance with the terms hereof are absolute and unconditional, irrespective of any action or inaction by the holder hereof to enforce the same, any waiver or consent with respect to any provision hereof, the recovery of any judgment against

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any person or entity or any action to enforce the same, or any setoff, counterclaim, recoupment, limitation or termination, or any breach or alleged breach by the holder hereof or any other Person of any obligation to the Company or any violation or alleged violation of law by the holder or any other Person, and irrespective of any other circumstance which might otherwise limit such obligation of the Company to the holder hereof in connection with the issuance of Warrant Shares. The Company will at no time close its shareholder books or records in any manner which interferes with the timely exercise of this Warrant.

21. Assignment, etc. The Warrantholder agrees that in no event will it make a transfer or disposition of any of this Warrant or the Warrant Shares (other than pursuant to an effective registration statement under the Securities Act), unless and until (i) it shall have notified the Company of the proposed disposition and shall have furnished the Company with a statement of the circumstances surrounding the disposition and assurance that the proposed disposition is in compliance with all applicable laws, and (ii) if reasonably requested by the Company, at the expense of such Warrantholder or its transferee, it shall have furnished to the Company an opinion of counsel, reasonably satisfactory to the Company, to the effect that such transfer may be made without registration under the Securities Act. Notwithstanding the foregoing, no formal notice or opinion of counsel shall be required for the transfer by an Warrantholder to any of the following (each, a “Permitted Transferee”): (x) any partner of a Warrantholder or to a retired partner of a Warrantholder, who retires after the date of this Warrant, (y) the estate of any such partner or a retired partner or for the transfer by gift, will or intestate succession of any partner to his spouse or lineal descendants or ancestors or (z) any entity which is a wholly-owned subsidiary of the Warrantholder or which is under common control with the Warrantholder; provided, however, in all cases where no legal opinion is required that the transferee shall agree in writing to be subject to the terms of this Warrant to the same extent as if it were the original Warrantholder hereunder.

IN WITNESS WHEREOF, the Company has caused this Common Stock Purchase Warrant to be duly executed as of the date first written above.

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