Exhibit 4.1

HEARTWARE INTERNATIONAL, INC.,

as Issuer

and

WILMINGTON TRUST, NATIONAL ASSOCIATION,

as Trustee

THIRD SUPPLEMENTAL INDENTURE

Dated as of August 23, 2016

to Indenture Dated as of

December 15, 2010

3.50% Convertible Senior Notes Due 2017

1.75% Convertible Senior Notes Due 2021

THIRD SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of August 23, 2016, between HeartWare International, Inc., a Delaware corporation (the “Company”), and Wilmington Trust, National Association (the “Trustee”), as trustee under the Indenture dated as of December 15, 2010, between the Company and the Trustee (the “Original Indenture”; the Original Indenture as amended and supplemented from time to time and as further amended and supplemented by this Supplemental Indenture, the “Indenture”).

W I T N E S S E T H:

WHEREAS, the Company and the Trustee have heretofore entered into the Original Indenture, as amended and supplemented by that certain First Supplemental Indenture, dated as of December 15, 2010, among the Company and the Trustee (the “First Supplemental Indenture”), to provide for the issuance of the Company’s 3.50% Convertible Senior Notes due 2017 (the “2017 Notes”), as further amended and supplemented by that certain Second Supplemental Indenture, dated as of May 13, 2015, among the Company and the Trustee (the “Second Supplemental Indenture” and, together with the First Supplemental Indenture and this Supplemental Indenture, the “Supplemental Indentures” and each, a “Supplemental Indenture”), to provide for the issuance of the Company’s 1.75% Convertible Senior Notes due 2021 (the “2021 Notes” and together with the 2017 Notes, the “Notes”),

WHEREAS, the Company, Medtronic, Inc., a Minnesota corporation (“Parent”) and Medtronic Acquisition Corp., a Delaware corporation and wholly-owned subsidiary of Parent (the “Purchaser”) entered into an Agreement and Plan of Merger, dated as of June 27, 2016 (the “Merger Agreement);

WHEREAS, pursuant to the Merger Agreement, on July 26, 2016, the Purchaser commenced a cash tender offer (the “Offer”) to purchase all of the outstanding Common Stock of the Company, at a purchase price of $58.00 per share of Common Stock, paid to the seller in cash, without interest, subject to any required withholding of taxes, upon the terms and subject to the conditions set forth in the Offer to Purchase, dated July 26, 2016, as amended, and Letter of Transmittal relating to the Offer;

WHEREAS, following the completion of the Offer and pursuant to the Merger Agreement, substantially simultaneously with the execution hereof, the Purchaser merged with and into the Company (the “Merger”) with the Company surviving the Merger as a wholly-owned subsidiary of Parent;

WHEREAS, pursuant to the Merger Agreement and subject to the terms and conditions therein, each share of Common Stock not purchased pursuant to the Offer and outstanding immediately prior to the effective time of the Merger (other than shares of Common Stock (i) owned by the Company as treasury stock or owned by Parent or Purchaser, which shares of Common Stock will be cancelled and retired and will cease to exist or (ii) held by a holder who properly demands appraisal for such shares of Common Stock in accordance with Section 262 of the Delaware General Corporation Law) will, by virtue of the Merger and without any action on the part of the holder thereof, be cancelled and converted into the right to receive an amount in cash, payable to the holder thereon, without any interest thereon, equal to $58.00 per share of Common Stock, paid to the seller in cash, without interest, subject to any required withholding of taxes (the “Merger Consideration”), upon the terms and subject to the conditions set forth in the Merger Agreement;

WHEREAS, in connection with the foregoing, Section 4.06 of each of the First Supplemental Indenture and the Second Supplemental Indenture provides that the Company and the Trustee shall execute a supplemental indenture under Section 7.01(f) of each of the First Supplemental Indenture and the Second Supplemental Indenture providing that, at and after the effective time of the Merger, for all conversions that occur after the effective date of the Merger, the right to convert each $1,000 principal amount of Notes shall be changed into a right to convert such principal amount of Notes into, and the consideration due upon conversion of each $1,000 principal amount of Notes shall be solely, cash in an amount equal to the Conversion Rate (as defined with respect to each series of Notes in the applicable Supplemental Indenture) in effect on the relevant Conversion Date (as defined with respect to each series of Notes in the applicable Supplemental Indenture), multiplied by the Merger Consideration;

WHEREAS, the Company desires that the Trustee join with it in the execution and delivery of this Supplemental Indenture, and in accordance with Sections 4.06, 7.04, 8.01 and 8.03 of each of the First Supplemental Indenture and the Second Supplemental Indenture and Sections 102 and 103 of the Original Indenture, has delivered an Officer’s Certificate and Opinion of Counsel to the Trustee responsive to and in compliance with the matters stated therein; and

WHEREAS, all conditions necessary to authorize the execution and delivery of this Supplemental Indenture have been complied with or have been done or performed by the Company.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, receipt of which is hereby acknowledged, the Company and the Trustee agree as follows for the equal and ratable benefit of each other and the Holders of the Notes:

(a) Capitalized terms used but not defined herein shall have the respective meanings assigned to them in the Original Indenture, as amended and supplemented by the First Supplemental Indenture and the Second Supplemental Indenture;

(b) Terms defined both herein and in the Original Indenture, as amended and supplemented by the First Supplemental Indenture and the Second Supplemental Indenture, shall have the meanings assigned to them herein; and

(c) Provisions of this Supplemental Indenture that conflict with or are otherwise inconsistent with provisions of the Original Indenture, as amended and supplemented by the First Supplemental Indenture and the Second Supplemental Indenture, shall be deemed to supersede and amend the Original Indenture, as amended and supplemented by the First Supplemental Indenture and the Second Supplemental Indenture, for all purposes with respect to the Notes.

[Signature page follows]

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the date first above written.

[Signature Page to HeartWare International, Inc. Third Supplemental Indenture]

[Signature Page to HeartWare International, Inc. Third Supplemental Indenture]