<PAGE>   1
                                                                     EXHIBIT 4.5

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

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

                                       AND

                                  HSBC BANK USA
                     (FORMERLY KNOWN AS MARINE MIDLAND BANK)

                                     TRUSTEE




                          SECOND SUPPLEMENTAL INDENTURE

                                   DATED AS OF

                               SEPTEMBER 10, 2001


                                       TO

                                    INDENTURE

                                   DATED AS OF

                                  APRIL 1, 1998

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

<PAGE>   2



SECOND 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 HSBC BANK USA
(formerly known as Marine Midland Bank), as Trustee (the "Trustee"), the office
of the Trustee at which at the date hereof its corporate trust business is
principally administered being 452 Fifth Avenue, New York, New York 10018.

                             RECITALS OF THE COMPANY

                  Pride International, Inc., a Louisiana corporation (the
"Company"), has executed and delivered to the Trustee an Indenture, dated as of
April 1, 1998, and a First Supplemental Indenture, dated as of April 24, 1998
(as so supplemented, the "Original Indenture," and as further supplemented by
this Second Supplemental Indenture, the "Indenture"), providing for the issuance
from time to time of the Company's unsecured subordinated 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 Second 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(1) of the Original Indenture provides that Pride
Delaware, as the surviving corporation of the Merger, is required to expressly
assume, by an indenture supplemental to the Original Indenture, 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 1514 of the Original Indenture, as it applies to the
Zero Coupon Convertible Subordinated Debentures due 2018 (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 Second Supplemental Indenture, to supplement and amend the
Original Indenture.

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

                  NOW, THEREFORE, THIS SECOND 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.

         Section 3. Ratification. The Indenture, as hereby amended and
supplemented, is ratified and confirmed in all respects. From and after the date
hereof, the Second 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 Second 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 Second Supplemental Indenture. The execution by the Trustee of this
Second 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 Second Supplemental Indenture. This Second 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 Second
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



                                          HSBC BANK USA, as Trustee



[CORPORATE SEAL]                            By /s/ Frank J. Godino
                                              ----------------------------------
                                                 Name:  Frank J. Godino
                                                 Title: Vice President