<PAGE>   1
                                                                     EXHIBIT 4.5

                FIRST AMENDMENT TO REGISTRATION RIGHTS AGREEMENT

         This First Amendment (this "Amendment"), dated as of June 1, 2001,
amends that certain Registration Rights Agreement (the "Agreement"), dated July
31, 1998, by and among MedCath Holdings, Inc., a Delaware corporation ("MedCath
Holdings"), and the several persons listed in Schedule I attached thereto (the
"Stockholders"). Capitalized terms used in this Amendment, but not otherwise
defined in this Amendment, shall have the meanings ascribed thereto in the
Agreement.

         WHEREAS, MedCath Holdings and MedCath Corporation ("MedCath
Corporation" or the "Company") plan to complete an internal reorganization (the
"Reorganization") by effecting (i) the exchange of the issued and outstanding
shares of MedCath Holdings' common stock, $.01 par value per share for an
equivalent number of shares of MedCath Corporation's common stock, $.01 par
value per share ("MedCath Corporation Common Stock") (the "MedCath Holdings
Exchange"); and (ii) the exchange of a portion of the interests held by
investors in certain heart hospitals for shares of MedCath Corporation Common
Stock (the "Hospitals Exchange" and, together with the MedCath Holdings
Exchange, the "Exchanges"), among other things;

         WHEREAS, contemporaneous with the consummation of the Reorganization
and the Exchanges, the Company plans to make an underwritten initial public
offering of shares of MedCath Corporation Common Stock (the "IPO"); and

         WHEREAS, MedCath Holdings, the Company and each of the Stockholders
desire to amend the Agreement to make certain arrangements among themselves with
respect to the matters set forth therein and herein.

         NOW, THEREFORE, in consideration of the premises and of the mutual
covenants and agreements herein contained, the parties hereto, intending to be
legally bound, hereby agree as follows:

         1.       Amendments

                  1.1      The parties hereby amend the Agreement to provide
         that from and after the date on which this Amendment is effective
         pursuant to Section 3 of this Amendment, all references to the
         "Company" in the Agreement shall mean MedCath Corporation.

                  1.2      The parties hereby amend Section 1 of the Agreement
         as follows:

                           1.2.1    By modifying the definition of "Common
                  Stock" to read in its entirety as follows:

                                    "Common Stock" shall mean the Common Stock,
                           $.01 par value per share, of the Company, as
                           constituted as of the date of the MedCath

<PAGE>   2

                           Holdings Exchange, subject to adjustment pursuant to
                           the provisions of Section 8 hereof.

                           1.2.2    By modifying the definition of "KKR Shares"
                  to read in its entirety as follows:

                                    "KKR Shares" shall mean the shares of Common
                           Stock received by MedCath 1998 LLC ("KKR Fund") in
                           the exchange of the issued and outstanding shares of
                           MedCath Holdings, Inc.'s common stock, $.01 par value
                           per share, for an equivalent number of shares of
                           Common Stock (the "Exchange") concurrent with and on
                           the date of consummation of the underwritten initial
                           public offering of shares of Common Stock (the
                           "IPO").

                           1.2.3    By modifying the definition of "WCAS Shares"
                  to read in its entirety as follows:

                                    "WCAS Shares" shall mean the shares of
                           Common Stock received by the persons listed on
                           Schedule I hereto under the heading "WCAS
                           Stockholders" in the Exchange concurrent with and on
                           the date of consummation of the IPO.

                  1.3      The parties hereby amend Section 2 of the Agreement
         by modifying Section 2 to read in its entirety as follows:

                           "2.      Restrictive Legend. Each certificate
         representing shares of Common Stock held by "affiliates" (as that term
         is defined in Rule 144 under the Securities Act of 1933, as amended) of
         MedCath Holdings or its subsidiaries prior to the MedCath Holdings
         Exchange, and each certificate issued upon exchange or transfer of any
         such securities, as the case may be, other than in a public sale, shall
         be stamped or otherwise imprinted with a legend substantially in the
         following form:

         "THE SHARES REPRESENTED BY THIS CERTIFICATE MAY NOT BE SOLD,
         TRANSFERRED OR OTHERWISE DISPOSED OF EXCEPT OR UNLESS: (1) COVERED BY
         AN EFFECTIVE REGISTRATION STATEMENT UNDER THE SECURITIES ACT OF 1933,
         AS AMENDED (THE "SECURITIES ACT"); (2) IN ACCORDANCE WITH RULE 145
         PROMULGATED UNDER THE SECURITIES ACT; OR (3) SOME OTHER EXEMPTION FROM
         REGISTRATION UNDER THE SECURITIES ACT IS AVAILABLE WITH RESPECT TO THE
         PROPOSED SALE, TRANSFER OR OTHER DISPOSITION.

                  1.4      The parties hereby amend Section 3(b) of the
         Agreement by modifying the penultimate sentence thereof, that begins
         with the words "The Company shall" in the tenth line from the bottom of
         Section 3(b), to read in its entirety as follows:


                                       2
<PAGE>   3

                  "The Company shall be obligated to register Restricted Stock
                  pursuant to this paragraph 3(b) on five (5) occasions (with
                  respect to requests by KKR Fund) and four (4) occasions (with
                  respect to requests by WCAS Fund VII) only and each demand
                  shall request registration of at least 15% of the amount of
                  Restricted Stock held by the requesting party and its
                  affiliates as of the date hereof."

                  1.5      The parties hereby amend the Agreement by deleting
         from the carry-over sentence immediately following the end of Section
         5(g) of the Agreement and beginning with the words "for purposes of
         paragraph (a) and (b) above" the following words in that carry-over
         sentence:

                  "or six months after the effective date thereof"

         and inserting in place thereof the following words:

                  "or, (i) in the case of any registration statement with an
                  effective date that is six months after but no more than nine
                  months after the date of consummation of the IPO (the "IPO
                  Closing"), until the first anniversary of the IPO Closing, and
                  (ii) in the case of any registration statement with an
                  effective date that is nine months or more after the IPO
                  Closing, for three months after the effective date thereof".

         2.       Ratification and Assumption. Except to the extent amended
hereby, the terms and provisions of the Agreement shall remain in full force and
effect and are ratified, confirmed and approved in all respects. MedCath
Corporation hereby accepts, agrees to, and acknowledges all such terms and
provisions, and agrees to assume all obligations of the Company under the
Agreement as if MedCath Corporation were the "Company" under the Agreement.

         3.       Effectiveness of Amendment. This Amendment shall become
effective as of the date on which the IPO is consummated and shall have no force
and effect unless and until the consummation of the IPO.

         4.       Reference. From and after the date hereof, each reference in
the Agreement and any other document describing or referencing the Agreement to
the "Agreement," "hereunder," "hereof," "herein," or words of like import
referring to the Agreement, shall mean and be a reference to the Agreement as
amended by this Amendment.

         5.       Binding Effect. This Amendment shall be binding upon and inure
to the benefit of the respective successors and assigns of the parties hereto.

         6.       Governing Law. This Amendment shall be governed by and
construed in accordance with New York law.

         7.       Counterparts. This Amendment may be executed in any number of
counterparts, each executed counterpart constituting an original but all
together only one instrument.


                                       3
<PAGE>   4

         IN WITNESS WHEREOF, each of the parties hereto has executed this
Agreement as a sealed instrument, all as of the day and year first above
written.

                                    MEDCATH HOLDINGS, INC.


                                    By:      /s/ David Crane
                                       -----------------------------------------
                                    Name:
                                    Title:

AGREED TO AND
ACCEPTED as of the
date first above written:


                                    MEDCATH CORPORATION


                                    By:      /s/ David Crane
                                       -----------------------------------------
                                    Name:
                                    Title:


                                    MEDCATH 1998 LLC


                                    By:      /s/ David H. S. Chung
                                       -----------------------------------------
                                    Name:    David H. S. Chung
                                    Title:   Vice President


                                       4
<PAGE>   5

                                    WCAS STOCKHOLDERS:

                                    WELSH, CARSON, ANDERSON
                                      & STOWE VII, L.P.

                                    By WCAS VII Partners, L.P.
                                    General Partner

                                    By:      /s/ Jonathan M. Rather
                                       -----------------------------------------
                                    Name: Jonathan M. Rather
                                    Title: General Partner



                                    WCAS HEALTHCARE PARTNERS, L.P.

                                    By: WCAS HP Partners
                                    General Partner

                                    By:      /s/ Jonathan M. Rather
                                       -----------------------------------------
                                    Name: Jonathan M. Rather
                                    Attorney-in-Fact



                                    Patrick J. Welsh
                                    Russell L. Carson
                                    Bruce K. Anderson
                                    Richard H. Stowe
                                    Andrew M. Paul
                                    Thomas E. McInerney
                                    Robert A. Minicucci
                                    Anthony J. de Nicola
                                    Paul B. Queally

                                    By:      /s/ Jonathan M. Rather
                                       -----------------------------------------
                                    Name: Jonathan M. Rather
                                    Attorney-in-Fact


                                       5
<PAGE>   6


                                    --------------------------------------------
                                    Lawrence B. Sorrell


                                    --------------------------------------------
                                    Rudolph E. Rupert


                                    --------------------------------------------
                                    D. Scott Mackesy


                                       6