<PAGE>   1
                                                                     EXHIBIT 4.4



================================================================================




                                 PM MERGER, INC.
        (BEING RENAMED PRIDE INTERNATIONAL, INC. PURSUANT TO THE MERGER)

                                       AND

                            THE CHASE MANHATTAN BANK

                                     TRUSTEE




                          FOURTH SUPPLEMENTAL INDENTURE

                                   DATED AS OF

                               SEPTEMBER 10, 2001


                                       TO

                                    INDENTURE

                                   DATED AS OF

                                   MAY 1, 1997

================================================================================
<PAGE>   2






                  FOURTH SUPPLEMENTAL INDENTURE, dated as of September 10, 2001,
between PM MERGER, INC., a Delaware corporation ("Pride Delaware"), having its
principal office at 5845 San Felipe, Suite 3300, Houston, Texas 77057, and THE
CHASE MANHATTAN BANK, as Trustee (the "Trustee"), the office of the Trustee at
which at the date hereof its corporate trust business is principally
administered being 450 West 33rd Street, 15th Floor, New York, New York 10001.

                             RECITALS OF THE COMPANY

                  Pride International, Inc., a Louisiana corporation (the
"Company"), has executed and delivered to the Trustee an Indenture, dated as of
May 1, 1997, a First Supplemental Indenture, dated as of May 1, 1997, a Second
Supplemental Indenture, dated as of May 26, 1999, and a Third Supplemental
Indenture, dated as of January 16, 2001 (as so supplemented, the "Original
Indenture," and as further supplemented by this Fourth Supplemental Indenture,
the "Indenture"), providing for the issuance from time to time of the Company's
unsecured senior debentures, notes or other evidences of indebtedness (the
"Securities"), issuable in one or more series as provided in the Indenture. All
capitalized terms used herein which are defined in the Original Indenture shall
have the meanings assigned thereto in the Original Indenture unless otherwise
defined herein.

                  Pursuant to an Agreement and Plan of Merger, dated as of May
23, 2001, between the Company, Pride Delaware, Marine Drilling Companies, Inc.,
a Texas corporation, and AM Merger, Inc., a Delaware corporation and wholly
owned subsidiary of the Company, the Company is, concurrently with the execution
and delivery of this Fourth Supplemental Indenture, merging with and into Pride
Delaware (the "Merger"), with Pride Delaware being the surviving corporation and
being renamed "Pride International, Inc."

                  Section 801(i) of the Original Indenture, as it applies to
each series of Securities outstanding, provides that Pride Delaware, as the
surviving corporation of the Merger, is required to expressly assume, by a
supplemental indenture, the due and punctual payment of the principal of (and
premium, if any) and interest on all the Securities and the performance of the
Company's covenants and obligations under the Original Indenture.

                  Section 1514 of the Original Indenture, as it applies to the
Zero Coupon Convertible Senior Debentures due 2021 (the "Convertible
Debentures"), provides that Pride Delaware, the person that, as of the effective
time of the Merger, is obligated to deliver securities upon conversion of the
Convertible Debentures, is required to enter into a supplemental indenture
providing that the Holder of a Convertible Debenture may convert it into the
kind and amount of securities, cash or other assets which such Holder would have
received immediately after the Merger if such Holder had converted the
Convertible Debenture immediately before the effective date of the Merger,
assuming (to the extent applicable) that such Holder (i) was not a constituent
Person or an Affiliate of a constituent Person to such transaction; (ii) made no
election with respect thereto; and (iii) was treated alike with the plurality of
non-electing Holders.


<PAGE>   3

                  Section 901(1) of the Original Indenture permits the execution
of supplemental indentures without the consent of any Holders to evidence the
succession of another Person to the Company and the assumption by any such
successor of the covenants of the Company in the Original Indenture and in the
Securities.

                  Pursuant to the foregoing authority, Pride Delaware proposes,
in and by this Fourth Supplemental Indenture, to supplement and amend the
Original Indenture.

                  All things necessary to make this Fourth Supplemental
Indenture a valid agreement of Pride Delaware, in accordance with its terms,
have been done.

                  NOW, THEREFORE, THIS FOURTH SUPPLEMENTAL INDENTURE WITNESSETH:

                  For and in consideration of the premises and the purchase of
the Securities by the Holders thereof, it is mutually covenanted and agreed, for
the equal and proportionate benefit of all Holders of the Securities or of
series thereof, as follows:

         Section 1. Succession by Merger. As of the effective time of the
Merger, (i) Pride Delaware shall become the successor to the Company for all
purposes of the Indenture, and (ii) Pride Delaware hereby expressly assumes the
due and punctual payment of the principal of (and premium, if any) and interest
(including Additional Amounts, if any) on all the Securities and the performance
of every covenant of the Indenture on the part of the Company to be performed or
observed.

         Section 2. Conversion. In accordance with Section 1514 of the Original
Indenture, as of the effective time of the Merger, the Convertible Debentures
shall be convertible into common stock, par value $.01 per share, of Pride
Delaware ("Pride Delaware Common Stock") in lieu of common stock, no par value,
of the Company, and the Holder of a Convertible Debenture may thereafter convert
it into the number of shares of Pride Delaware Common Stock that such Holder
would have received immediately after the Merger if such Holder had converted
the Convertible Debenture immediately before the effective time of the Merger,
assuming that such Holder was not a constituent Person or an Affiliate of a
constituent Person to such transaction. This conversion right shall be subject
to adjustment on the same terms as provided in Article Fifteen of the Original
Indenture as it applies to the Convertible Debentures.

         Section 3. Ratification. The Indenture, as hereby amended and
supplemented, is ratified and confirmed in all respects. From and after the date
hereof, the Fourth Supplemental Indenture shall form a part of the Indenture for
all purposes, and every Holder of Securities heretofore or hereafter
authenticated and delivered shall be bound hereby. All recitations or recitals
contained in this Fourth Supplemental Indenture are made by and on behalf of
Pride Delaware only, and the Trustee is in no way responsible for the
correctness of any statement herein contained or for the validity or sufficiency
of this Fourth Supplemental Indenture. The execution by the Trustee of this
Fourth Supplemental Indenture shall not be construed to be an approval or
disapproval by the Trustee of the advisability of the action being taken herein
by



<PAGE>   4

Pride Delaware. All the provisions of the Indenture with respect to the rights,
privileges, immunities, powers and duties of the Trustee shall be applicable in
respect hereof as fully and with like effect as if set forth herein in full with
such omissions, variations or insertions, if any, as may be appropriate to make
the same conform to this Fourth Supplemental Indenture. This Fourth Supplemental
Indenture shall be governed by and construed in accordance with the laws of the
State of New York.


                                      * * *


                  This instrument may be executed in any number of counterparts,
each of which so executed shall be deemed to be an original, but all such
counterparts shall together constitute but one and the same instrument.



<PAGE>   5



                  IN WITNESS WHEREOF, the parties hereto have caused this Fourth
Supplemental Indenture to be duly executed, and their respective corporate seals
to be hereunto affixed and attested, all as of the day and year first above
written.

                                      PM MERGER, INC., being renamed Pride
                                      International, Inc. pursuant to the Merger



[CORPORATE SEAL]                      By  /s/ Paul A. Bragg
                                        ----------------------------------------
                                        Name:  Paul A. Bragg
                                        Title: President and Chief Executive
                                               Officer



                                      THE CHASE MANHATTAN BANK, as Trustee



[CORPORATE SEAL]                      By /s/ Larry O'Brien
                                         --------------------------------------
                                         Name:  Larry O'Brien
                                         Title: Vice President