AMENDMENT TO THE RIGHTS AGREEMENT

Exhibit 4.1

EXECUTION COPY

AMENDMENT TO THE RIGHTS AGREEMENT

THIS AMENDMENT dated as of July 29, 2013 (this “Amendment”), amends the Rights Agreement, dated as of May 24, 2013 (the “Rights Agreement”), by and between Health Management Associates, Inc., a Delaware corporation (the “Corporation”), and American Stock Transfer & Trust Company, LLC, a New York limited liability trust company (the “Rights Agent”). All capitalized terms used but not defined in this Amendment shall have the meanings ascribed to them in the Rights Agreement.

WHEREAS, the Corporation has entered into an Agreement and Plan of Merger (the “Merger Agreement”) with Community Health Systems, Inc. (“Parent”) and FWCT-2 Acquisition Corporation (“Merger Sub”), dated as of July 29, 2013, pursuant to which, among other things, (a) Merger Sub shall be merged with and into the Corporation (the “Merger”), whereupon the separate corporate existence of Merger Sub shall cease and the Corporation shall be the surviving corporation (the “Surviving Corporation”) and a direct or indirect wholly owned subsidiary of Parent and (b) each share of the common stock of the Corporation issued and outstanding immediately prior to the Effective Time (as defined in the Merger Agreement) (other than Dissenting Shares (as defined in the Merger Agreement) or shares cancelled or converted into shares of the Surviving Corporation in accordance with the Merger Agreement) will be automatically converted into and thereafter represent the right to receive the Merger Consideration (as defined in the Merger Agreement);

WHEREAS, pursuant to resolutions adopted on July 29, 2013 (the “Board Resolutions”), the board of directors of the Corporation (the “Board”) has adopted and approved the Merger Agreement;

WHEREAS, Section 26 of the Rights Agreement provides that for so long as the Rights are redeemable (subject to the third sentence of Section 26), the Rights Agent shall, if the Corporation so directs, supplement or amend any provision of the Rights Agreement without the approval of any holders of the Rights;

WHEREAS, the Rights are currently redeemable and no person is an Acquiring Person;

WHEREAS, pursuant to the Board Resolutions, and in connection with entering into the Merger Agreement, the Board has unanimously determined that an amendment to the Rights Agreement is advisable, fair to and in the best interests of the Corporation and its stockholders; and

WHEREAS, subject to and in accordance with the terms of this Amendment, the Corporation has directed, and the Rights Agent has agreed, to amend the Rights Agreement in certain respects, as more particularly set forth herein.

NOW, THEREFORE, in accordance with the procedures for amendment of the Agreement set forth in Section 26 thereof, and in consideration of the promises and the mutual agreements herein set forth, the parties hereto hereby agree as follows:

“Notwithstanding anything in this Agreement to the contrary, none of Community Health Systems, Inc., a Delaware corporation (“Parent”), FWCT-2 Acquisition Corporation, a newly formed Delaware corporation and direct or indirect wholly owned subsidiary of Parent (“Merger Sub”) or their Subsidiaries, Affiliates or Associates shall be, or shall be deemed to be, an Acquiring Person for purposes of this Agreement by virtue of one or more of (i) the adoption, approval, execution or delivery of the Agreement and Plan of Merger, dated as of July 29, 2013, by and among the Corporation, Parent and Merger Sub (the “Merger Agreement”), (ii) the public or other announcement of the Merger Agreement or any of the transactions contemplated by the Merger Agreement (including the Merger (as defined in the Merger Agreement)), or (iii) the consummation of the Merger or any of the other transactions contemplated by the Merger Agreement (each such event, an “Exempt Event”)”

“; provided, however, that notwithstanding anything in this Agreement to the contrary, a Stock Acquisition Date shall not occur and shall not be deemed to have occurred as the result of an Exempt Event.”

“; provided, however, that notwithstanding anything in this Agreement to the contrary, a Distribution Date shall not occur and shall not be deemed to have occurred as the result of an Exempt Event.”

“(e) Nothing in this Agreement shall be construed to give any holder of Rights or any other Person any legal or equitable rights, remedies or claims under this Agreement by virtue of an Exempt Event.”

“(i) the earlier of May 24, 2014 or immediately prior to the Effective Time (as defined in the Merger Agreement) (the earlier being herein referred to as the “Final Expiration Date”)”

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“(iv) Notwithstanding anything in this Agreement to the contrary, in no event shall any Exempt Event be, or be deemed to be, or result in, any event described in Section 11(a)(ii) hereof, and this Section 11(a) shall not apply to any Exempt Event.”

“(f) Notwithstanding anything in this Agreement to the contrary, in no event shall any Exempt Event be, or be deemed to be, or result in any event described in Section 13(a) hereof, and this Section 13 shall not apply to any Exempt Event.”

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