<PAGE>

                                                                   Exhibit 10.40


                                THIRD AMENDMENT
                                    TO THE
                      HEALTH MANAGEMENT ASSOCIATES, INC.
                    SUPPLEMENTAL EXECUTIVE RETIREMENT PLAN


          WHEREAS, Health Management Associates, Inc., a corporation under the
laws of the State of Delaware (the "Company"), established the Health Management
Associates, Inc. Supplemental Executive Retirement Plan (the "Plan");

          WHEREAS, the right to amend the Plan is expressly reserved to the
Company under Section 5.3 thereof;

          WHEREAS, the Plan was amended effective December 13, 1993, under the
First Amendment to the Health Management Associates, Inc. Supplemental Executive
Retirement Plan;

          WHEREAS, the Plan was amended effective September 17, 1996, under the
Second Amendment to the Health Management Associates, Inc. Supplemental
Executive Retirement Plan;

          WHEREAS, the Company wishes to amend the Plan again.

          NOW, THEREFORE, the Plan is hereby amended, effective the 19th day of
September, 2000, as follows:

          1.   Section 2.1 is amended to read as follows:

               Section 2.1. "Actuarial Equivalent" means a benefit having the
          same value as the benefit which such Actuarial Equivalent replaces.
          The determination of any Actuarial Equivalent shall be based on the
          following actuarial assumptions: (a) the annual rate of interest on
          10-year Treasury securities in effect as of the first day of the month
          for which an Actuarial Equivalent is determined and (b) the 1984
          Unisex Pension Mortality Table.

          2.   Section 2.4 is amended to read as follows:

               Section 2.4. "Change of Ownership" means (a) the acquisition
          after the Effective Date, whether directly, indirectly, beneficially
          (within the meaning of Rule 13d-3 of the Securities Exchange Act of
          1934, as amended (the "1934 Act")), or of record, of securities of the
          Company or its parent corporation, HMA Holding Corp., by any "person"
          (within the meaning of Sections 13(d) and 14(d)(2) of the 1934 Act),
          including any corporation or group of associated persons acting in
          concert which, after such acquisition will result in such person
          having control of the Company or HMA Holding Corp., or (b) a change in
          the ownership of a substantial portion of the assets of the Company or
          HMA Holding Corp. within the meaning of Section 280G of the Internal
          Revenue Code of 1986, as amended. Notwithstanding the immediately
          preceding sentence, a Change of Ownership shall not be deemed to have
          occurred if such acquisition is by (i) the Company; and/or (ii) any
          employee pension benefit plan (within the meaning of Section 3(2) of
          the Employee Retirement Income Security Act of 1974, as amended) of
          the Company, including a trust established pursuant to any such plan;
          and/or (iii) any person who is a stockholder of HMA Holding Corp. on
          the Effective Date, or any person who is the spouse of such
          stockholder, or any person who, directly or indirectly, through one or
          more intermediaries, controls or is controlled by, or is under common
          control of such stockholder. For purposes of this Section "control"
          means the ownership of more than twenty-five percent (25%) of the
          voting authority with respect to the Company, HMA Holding Corp. or any
          such person

                                      62
<PAGE>

          within the context of clause (b)(iii) of this Section, as the case may
          be.

          3.   Section 2.19 is hereby added to read as follows:

               Section 2.19. "Trust" means a "rabbi trust" that does not
          affect the unfunded status of this Plan and whose form follows
          guidance promulgated by the Internal Revenue Service in Revenue
          Procedure 92-64, as it may be amended from time to time.

          4.   Section 4.4 is amended to read as follows:

               Section 4.4. Change of Ownership. Notwithstanding Sections
                            -------------------
          4.1, 4.2 or 4.3, the following provisions shall apply in the event the
          Board gains knowledge that a Change of Ownership has occurred or is
          likely to occur:

                    (a)  If such an event occurs after a Participant's
          Normal Retirement Date, the Company shall immediately pay the single
          cash sum Actuarial Equivalent of the Participant's Retirement Benefit
          to such Participant or his Beneficiary.

                    (b)  If such an event occurs before a Participant's
          Normal Retirement Date, the Company shall immediately deposit with
          trustee of the Trust an amount equal to the Actuarial Equivalent of
          the Participant's Retirement Benefit. Such a deposit shall be
          calculated based upon the Participant's age at the time of such
          deposit. In the event of such a Participant's subsequent termination
          from Full-Time Employment, for any reason including death, the trustee
          of the Trust shall immediately distribute the amount of such deposit,
          plus earnings thereon, to the Participant or his Beneficiary.

                    (c)  If no Trust has been previously established under
          this Plan, the Company shall establish a Trust immediately upon the
          Board gaining knowledge that a Change of Ownership has occurred or is
          likely to occur.

                    (d)  The Company shall compensate the Participant or his
          Beneficiary on an after-tax basis for:

                         (i)     Medicare or FICA taxes;

                         (ii)    the increase in the effective rate of federal
               and state income taxes stemming from the lump sum payment;
               and

                         (iii)   any excise taxes

               which shall be payable with respect to any payments made
               hereunder as a result of a Change of Ownership.

                    (e)  With respect to amounts determined pursuant to
               subsection (d):

                         (i)     if a Participant has reached his Normal
               Retirement Date, the Company shall pay the amounts directly
               to such Participant; and

                         (ii)    if a Participant has not yet reached
               his Normal Retirement Date, the Company shall make an additional
               cash deposit to the trustee of the Trust equal to the amounts
               determined under subsection (d) based upon the tax rates in
               effect for the Participant on the date of the deposit. At the
               time such a Participant or Beneficiary receives payment from the
               Trust, the trustee shall distribute the additional estimated cash
               deposit, with any earnings thereon, directly to such Participant
               or Beneficiary to the extent necessary to compensate the
               Participant or Beneficiary for the actual tax liability
               (including the tax liability for the additional payment). If the
               aforementioned distribution is insufficient to compensate such
               Participant or Beneficiary for the actual tax

                                      63
<PAGE>

                    liability (including the tax liability for the additional
                    payment), the Company shall make an additional direct cash
                    payment to the Participant or Beneficiary equal to the
                    shortfall. Any assets remaining in the Trust after a
                    Participant or Beneficiary has received the Retirement
                    Benefit calculated pursuant to subsection (b) and has been
                    compensated for the tax liability shall be returned to the
                    Company.

                           (f)   Upon full payment pursuant to this Section, no
          further benefits shall be payable under the Plan to such Participant.

          5.   Section 6.2 is amended to read as follows:

               Section 6.2. Title to Plan Assets. Title to and beneficial
                            --------------------
          ownership of any assets, whether cash or investments, which are held
          or earmarked to pay the deferred compensation obligation hereunder,
          shall at all times remain unrestricted assets of the Company and any
          Participant or Beneficiary (or personal representative) shall not have
          any property interest in such assets. However, the Company, may
          establish a Trust under this Plan and deposit any assets, whether cash
          or investments, therein for the benefit of the Participants or
          Beneficiaries. Title to and beneficial ownership of the assets of the
          Trust shall be held by the trustees of such Trust. This Plan at all
          times shall be considered entirely unfunded both for federal tax
          purposes and for purposes of Title I of the Employee Retirement Income
          Security Act of 1974, as amended. To the extent that any Participant
          or Beneficiary (or personal representative) acquires a right to
          receive payments from the Company, such right shall be no greater than
          the right of any unsecured general creditor of the Company.

          6.   Section 6.3 is amended to add the following sentence to the end
               thereof:

          Notwithstanding the foregoing, nothing herein shall preclude the
          Company from transferring any life insurance contract to a Trust
          established hereunder, or designating the trustee as beneficiary of
          any such contract.

          The remainder of the Plan shall remain in full force and effect and
shall be unaffected by this Third Amendment.

          IN WITNESS WHEREOF, the Company has caused this Third Amendment to be
executed this 5th day of December, 2000.

                                        HEALTH MANAGEMENT ASSOCIATES,  INC.



                                        By: /s/ Timothy R. Parry
                                           ------------------------------------


                                        Its:    Vice President
                                            -----------------------------------


                                      64