Exhibit 10.4

Conformed Copy

FIRST SUPPLEMENTAL INDENTURE

This First Supplemental Indenture (“Supplemental Indenture”) is made as of November 4, 2011, by and among Kinetic Concepts, Inc., a Texas corporation, as issuer (the “Issuer”), KCI USA, Inc., a Delaware corporation, as subsidiary guarantor (the “Subsidiary Guarantor”), and U.S. Bank National Association, a national banking association, as trustee (the “Trustee”) under the Indenture referred to below.

W I T N E S S E T H

WHEREAS, the Issuer, the Subsidiary Guarantor and the Trustee are parties to that certain Indenture, dated as of April 21, 2008 (the “Indenture”), pursuant to which the Issuer issued its 3.25% Convertible Senior Notes due 2015 (the “Notes”); and

WHEREAS, pursuant to the Agreement and Plan of Merger, dated as of July 12, 2011 (the “Merger Agreement”), by and among the Issuer, Chiron Holdings, Inc., a Delaware corporation (“Chiron”), and Chiron Merger Sub, Inc., a Texas corporation and a direct wholly owned subsidiary of Chiron (“Chiron Merger Sub”), Chiron Merger Sub will merge with and into the Issuer (the “Merger”) and the Issuer will continue as the surviving corporation; and

WHEREAS, Section 15.06 of the Indenture provides that, subject to certain exceptions, in connection with any merger to which the Company is a party, the Company shall execute with the Trustee a supplemental indenture providing that from and after the date of such supplemental indenture, the right of holders of Notes then outstanding to convert each $1,000 principal amount of Notes into cash and shares of Common Stock will be changed to a right to convert such Note into the kind and amount of shares of stock, other securities or other property or assets (including cash or any combination thereof) that a holder of a number of shares of Common Stock equal to the applicable Conversion Rate prior to the Merger would have owned or been entitled to receive (the “Reference Property”) upon the consummation of such merger; and

WHEREAS, pursuant to the Merger Agreement and subject to the terms and conditions set forth therein, at the effective time of the Merger, the Company’s Common Stock will be converted into the right to receive $68.50 per share, less any applicable withholding taxes and without any interest thereon; 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.

NOW, THEREFORE, in consideration of the foregoing and for other good and valuable consideration, receipt of which is hereby acknowledged, the Issuer, the Subsidiary Guarantor and the Trustee agree as follows for the equal and ratable benefit of the Noteholders:

ARTICLE 1

Definitions

Section 1.01. General. Capitalized terms used but not defined herein shall have the meanings assigned to them in the Indenture.

ARTICLE 2

Agreements of Parties

Section 2.01. Daily VWAP. The definition of Daily VWAP in the Indenture is hereby amended and restated in its entirety as follows:

“Daily VWAP” means $68.50.

Section 2.02 Conversion of Notes. In accordance with Section 15.06 of the Indenture, from and after the date of this Supplemental Indenture, the holders of Notes then outstanding shall have the right, during the period such Notes shall be convertible as specified in the Indenture, to convert such Notes solely into the Reference Property (which for the avoidance of doubt, shall be equal to $1,334.13 per $1,000 aggregate principal amount of the Notes based on a Conversion Rate of 19.4764. Noteholders electing to convert their Notes from and after the effective time of the Merger up to and including the close of business on the Business Day immediately prior to the related Fundamental Change Purchase Date will be entitled to receive $1,456.30 per $1,000 aggregate principal amount of the Notes based on a Conversion Rate of 21.2598, which includes a Conversion Rate increase of 1.7834 corresponding to the Make-Whole Conversion Rate Adjustment). Accordingly, any reference to a share of Common Stock in the Indenture shall be deemed a reference to an amount in cash equal to $68.50 (without interest), and the provisions of the Indenture, as modified herein, including, for the avoidance of doubt, Section 15.03, shall continue to apply with the necessary changes having been made to the Noteholders’ right to convert the Notes into the Reference Property.

ARTICLE 3

Miscellaneous Provisions

Section 3.01 Effectiveness; Construction. This Supplemental Indenture shall become effective upon its execution and delivery by the Issuer and the Trustee and as of the date hereof. Upon such effectiveness, the Indenture shall be supplemented in accordance herewith. This Supplemental Indenture shall form a part of the Indenture for all purposes, and every Noteholder heretofore or hereafter authenticated and delivered under the Indenture shall be bound thereby. The Indenture and this Supplemental Indenture shall henceforth be read and construed together.

Section 3.02 Indenture Remains in Full Force and Effect. Except as supplemented hereby, all provisions in the Indenture shall remain in full force and effect.

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Section 3.03 Trustee Matters. The Trustee accepts the Indenture, as supplemented hereby, and agrees to perform the same upon the terms and conditions set forth therein, as supplemented hereby. The Trustee shall be entitled to the benefit of every provision of the Indenture relating to the conduct or affecting the liability or affording protection to the Trustee, whether or not elsewhere herein so provided. The recitals contained in this Supplemental Indenture shall be taken as the statements of the Issuer and the Trustee assumes no responsibility for their correctness. The Trustee makes no representation as to the validity or sufficiency of this Supplemental Indenture.

Section 3.04 No Third-Party Beneficiaries. Nothing in this Supplemental Indenture, express or implied, shall give to any Person, other than the parties to the Indenture, as supplemented hereby, any Paying Agent, any Conversion Agent, any authenticating agent, any Note Registrar and their successors, and to the Noteholders, any benefit of any legal or equitable right, remedy or claim under the Indenture, as supplemented hereby.

Section 3.05 Severability. In the event any provision of this Supplemental Indenture shall be invalid, illegal or unenforceable, then (to the extent permitted by law) the validity, legality or enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

Section 3.06 Headings. The article and section headings of this Supplemental Indenture have been inserted for convenience of reference only and are not to be considered a part of this Supplemental Indenture and shall in no way modify or restrict any of the terms or provisions hereof.

Section 3.07 Successors. All agreements of the Issuer and the Trustee in this Supplemental Indenture shall bind their respective successors and assigns whether so expressed or not.

Section 3.09 Governing Law. This Supplemental Indenture shall be deemed to be a contract made under the laws of New York, and for all purposes shall be construed in accordance with the laws of New York, without regard to conflicts of law principles thereof.

Section 3.10 Counterpart Signatures. This Supplemental Indenture may executed in any number of counterparts, each of which shall be an original, but such counterparts shall together constitute but one and the same instrument.

[Signatures follow]

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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 First Supplemental Indenture]