<PAGE>

                                                                     EXHIBIT 4.1


                                SECOND AMENDMENT

                  SECOND AMENDMENT (this "Amendment"), dated as of November 24,
2004, among NOBLE CORPORATION, a Cayman Islands exempted company limited by
shares ("Parent"), NOBLE HOLDING (U.S.) CORPORATION, a Delaware corporation
("NHC" and, together with Parent, the "Parent Guarantors"), NOBLE DRILLING
CORPORATION, a Delaware corporation (the "Borrower"), various lending
institutions party to the Credit Agreement referred to below (the "Lenders"),
Wells Fargo Bank, N.A. (as successor to Wells Fargo Bank Texas, National
Association) and SunTrust Bank, as Documentation Agents, The Bank of
Tokyo-Mitsubishi, Ltd. and Westdeutsche Landesbank Girozentrale, New York
Branch, as Syndication Agents, The Bank of Tokyo-Mitsubishi, Ltd. and Nordea
Bank Finland Plc, New York Branch, as Co-Lead Arrangers, Nordea Bank Finland
Plc, New York Branch, as Bookrunner, and NORDEA BANK FINLAND PLC, NEW YORK
BRANCH (as the replacement Administrative Agent to Nordea Bank Norge ASA, New
York Branch, as successor by merger to Christiania Bank og Kreditkasse ASA, New
York Branch), as Administrative Agent (the "Administrative Agent"). All
capitalized terms used herein and not otherwise defined shall have the meanings
assigned such terms in the Credit Agreement referred to below.

                               W I T N E S E T H :

                  WHEREAS, the Parent Guarantors, the Borrower, the Lenders, the
Documentation Agents, the Syndication Agents and the Administrative Agent are
parties to a Credit Agreement, dated as of May 30, 2001 and amended and restated
as of May 1, 2002 (as amended and restated further, amended, modified or
supplemented to the date hereof, the "Credit Agreement");

                  WHEREAS, subject to the terms and conditions set forth herein,
the parties hereto wish to amend the Credit Agreement as herein provided;

                  NOW, THEREFORE, it is agreed:

                  1. Section 1.14(a) of the Credit Agreement is hereby amended
by deleting the amount "$200,000,000" appearing therein and inserting the text
"$100,000,000" in lieu thereof.

                  2. The definition of "Maturity Date" appearing in Section 11
of the Credit Agreement is hereby amended by deleting said definition in its
entirety and inserting the following new definition in lieu thereof:

                  "Maturity Date" shall mean November 30, 2009.

                  3. The definition of "Total Commitment" appearing in Section
11 of the Credit Agreement is hereby amended by deleting the text "on the
Restatement Effective Date shall be $200,000,000" and inserting the text "on the
Second Amendment Effective Date shall be $300,000,000" in lieu thereof.


<PAGE>

                  4. Section 11 of the Credit Agreement is hereby further
amended by inserting in the proper alphabetical order the following new
definitions:

                  "Second Amendment" shall mean the Second Amendment to this
                  Agreement, dated as of November 24, 2004.

                  "Second Amendment Effective Date" shall have the meaning set
                  forth in the Second Amendment.

                  5. The Credit Agreement is hereby further amended by deleting
Annex I thereto in its entirety and inserting in lieu thereof a new Annex I in
the form of Annex I attached hereto.

                  6. Each of the Parent Guarantors, the Borrower, and the
Lenders hereby agree that Nordea Bank Finland Plc, New York Branch, shall
replace Nordea Bank Norge ASA, New York Branch, as Administrative Agent under
the Credit Agreement and the other Credit Documents.

                  7. In order to induce Lenders to enter into this Amendment,
Parent (x) represents and warrants that no Default or Event of Default exists on
the Second Amendment Effective Date (as hereinafter defined) both before and
after giving effect to this Amendment, and (y) makes each of the
representations, warranties and agreements contained in the Credit Agreement and
the other Credit Documents on and as of the Second Amendment Effective Date both
before and after giving effect to this Amendment (it being understood that any
representation or warranty which by its terms is made as of a specified date
shall be required to be true and correct in all material respects as of such
date).

                  8. This Amendment is limited as specified and shall not
constitute a modification, acceptance or waiver of any other provision of the
Credit Agreement or any other Credit Document.

                  9. This Amendment may be executed in any number of
counterparts and by the different parties hereto on separate counterparts, each
of which counterparts when executed and delivered shall be an original, but all
of which shall together constitute one and the same instrument. A complete set
of counterparts shall be lodged with the Borrower and the Administrative Agent.

                  10. THIS AMENDMENT AND THE RIGHTS AND OBLIGATIONS OF THE
PARTIES HEREUNDER SHALL BE CONSTRUED IN ACCORDANCE WITH AND GOVERNED BY THE LAW
OF THE STATE OF NEW YORK.

                  11. This Amendment shall become effective on the first date
(the "Second Amendment Effective Date") on which each of the following
conditions have been met:

                  (i) the Administrative Agent shall have received for the
         account of each Lender requesting the same a Note in an amount of such
         Lender's Commitment after giving effect to this Amendment;


                                      - 2 -

<PAGE>

                  (ii) the Administrative Agent shall have received from the
         Parent Guarantors and the Borrower true and correct certified copies of
         resolutions of the Board of Directors of such Credit Party with respect
         to this Amendment, and such resolutions shall in form and substance
         satisfactory to the Administrative Agent;

                  (iii) the Administrative Agent shall have received from (x)
         Thompson & Knight, LLP, counsel to the Parent Guarantors and the
         Borrower, an opinion addressed to the Administrative Agent and each of
         the Lenders and dated the Second Amendment Effective Date, and (y)
         Maples and Calder, special counsel to Parent, an opinion addressed to
         the Administrative Agent and each of the Lenders and dated the Second
         Amendment Effective Date, in each case covering such matters incident
         to this Amendment and the Additional Loans as the Administrative Agent
         may reasonably request and otherwise in form and substance satisfactory
         to the Administrative Agent;

                  (iv) the Borrower shall have, in coordination with the
         Administrative Agent, repaid outstanding Loans of certain of the
         Lenders, and incur additional Loans from certain other Lenders, in each
         case to the extent necessary so that all of the Lenders participate in
         each outstanding Borrowing of Loans pro rata on the basis of their
         respective Commitments and with the Borrower being obligated to pay to
         the Administrative Agent for the account of the respective Lenders any
         costs of the type referred to in Section 1.11 in connection with any
         such repayment and/or Borrowing (it being understood that all
         repayments and incurrences of Loans shall be effected by the
         Administrative Agent through inter-lender transfers between the
         Lenders); and

                  (v) the Borrower, the Parent Guarantors, the Administrative
         Agent and each Lender shall have signed a counterpart hereof (whether
         the same or different counterparts) and shall have delivered (including
         by way of facsimile transmission) the same to the Administrative Agent
         at its Notice Office.

                  12. Each Lender party hereto which was not an original party
to the Credit Agreement (each a "New Lender") (i) confirms that it has received
a copy of the Credit Agreement and the other Credit Documents, together with
copies of the financial statements referred to therein and such other documents
and information as it has deemed appropriate to make its own credit analysis and
decision to enter into this Agreement and to become a Lender under the Credit
Agreement, (ii) agrees that it will, independently and without reliance upon the
Administrative Agent or any other Lender and based on such documents and
information as it shall deem appropriate at the time, continue to make its own
credit decisions in taking or not taking action under the Credit Agreement,
(iii) agrees that it will perform in accordance with their terms all of the
obligations which by the terms of the Credit Agreement are required to be
performed by it as a Lender, and (iv) in the case of each lending institution
organized under the laws of a jurisdiction outside the United States, attaches
the applicable forms described in Section 4.04(b) certifying as to its
entitlement to a complete exemption from United States withholding taxes with
respect to all payments to be made under the Credit Agreement and the other
Credit Documents. On and after the Second Amendment Effective Date, each New
Lender (i) shall be obligated to make the Loans provided to be made by it as
provided in the Credit Agreement on the terms, and subject to the conditions,
set forth in the Credit Agreement, and


                                      - 3 -

<PAGE>

shall become a Lender pursuant to the Credit Agreement and (ii) shall have the
rights and obligations of a Lender thereunder and under the other Credit
Documents.

                  13. So long as the Second Amendment Effective Date occurs, the
Borrower shall pay to the Administrative Agent for the account of each Lender,
an amendment fee equal to the sum of (i) 0.1225% of the amount of such Lenders'
Commitment immediately prior to the Second Amendment Effective Date (or, if
less, the amount of such Lenders' Commitment after giving effect to the Second
Amendment Effective Date) and (ii) 0.175% of the amount by which the amount of
such Lenders' Commitment after giving effect to the Second Amendment Effective
Date exceeds the amount of such Lenders' Commitment immediately prior to the
Second Amendment Effective Date. All fees payable pursuant to the immediately
preceding sentence shall be paid to the Administrative Agent within one Business
Day after the Second Amendment Effective Date, which fees shall be distributed
by the Administrative Agent to the relevant Lenders in the amounts specified in
the immediately preceding sentence.

                  14. The Borrower hereby agrees to pay to the Administrative
Agent and the Lenders all fees, costs and expenses (including, without
limitation, legal fees and expenses and any breakage costs incurred as a result
of the repayment of Loans as contemplated by Section 11(iv) hereof) payable to
the Administrative Agent and the Lenders within five Business Days following the
receipt of an invoice for such fees, costs and expenses.

                  15. At all times on and after the Second Amendment Effective
Date, all references in the Credit Agreement and each of the Credit Documents to
the Credit Agreement shall be deemed to be references to the Credit Agreement
after giving effect to this Amendment.


                                      * * *


                                     - 4 -
<PAGE>
         IN WITNESS WHEREOF, each of the parties hereto has caused a counterpart
of this Amendment to be duly executed and delivered as of the date first above
written.


                                             NOBLE DRILLING CORPORATION

                                             By /s/ Mark L. Mey
                                               ---------------------------------
                                               Name: Mark L. Mey
                                               Title: Vice President & Treasurer


                                             NOBLE CORPORATION

                                             By /s/ Mark A. Jackson
                                               ---------------------------------
                                               Name: Mark A. Jackson
                                               Title: Senior VP & CFO


                                             NOBLE HOLDING (U.S.) CORPORATION

                                             By /s/ Mark A. Jackson
                                               ---------------------------------
                                               Name: Mark A. Jackson
                                               Title: Senior VP & CFO
<PAGE>
                                             NORDEA BANK FINLAND PLC,
                                              NEW YORK BRANCH,
                                             as Administrative Agent


                                             By /s/ Hans Christian Kjelsrud
                                               ---------------------------------
                                               Name: Hans Christian Kjelsrud
                                               Title: Senior Vice President


                                             By /s/ Alison B. Barber
                                               ---------------------------------
                                               Name: Alison B. Barber
                                               Title: Vice President


                                             NORDEA BANK NORGE ASA,
                                              GRAND CAYMAN BRANCH,
                                             as Lender


                                             By /s/ Hans Christian Kjelsrud
                                               ---------------------------------
                                               Name: Hans Christian Kjelsrud
                                               Title: Senior Vice President


                                             By /s/ Alison B. Barber
                                               ---------------------------------
                                               Name: Alison B. Barber
                                               Title: Vice President
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS BOOKRUNNER, AND
                                      NORDEA BANK FINLAND PLC, NEW YORK BRANCH,
                                      AS ADMINISTRATIVE AGENT.

                                      NAME OF INSTITUTION:

                                      The Bank of Tokyo-Mitsubishi Limited


                                      By: /s/ KELTON GLASSCOCK
                                          --------------------------------
                                          Name: Kelton Glasscock
                                          Title: Vice President & Manager
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS BOOKRUNNER, AND
                                      NORDEA BANK FINLAND PLC, NEW YORK BRANCH,
                                      AS ADMINISTRATIVE AGENT.

                                      NAME OF INSTITUTION:

                                      SUNTRUST BANK


                                      By: /s/ JOE McCREERY
                                          --------------------------------
                                          Name:  Joe McCreery
                                          Title: Vice President
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS BOOKRUNNER, AND
                                      NORDEA BANK FINLAND PLC, NEW YORK BRANCH,
                                      AS ADMINISTRATIVE AGENT.

                                      NAME OF INSTITUTION:

                                      Wells Fargo Bank, N.A.


                                      By: /s/ P. C. LAUINGER III
                                          --------------------------------
                                          Name:  Philip C. Lauinger III
                                          Title: Vice President
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, AND NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS ADMINISTRATIVE
                                      AGENT.

                                      NAME OF INSTITUTION:

                                      WESTLB AG, New York Branch


                                      By: /s/ WALTER T. DUFFY III
                                          --------------------------------
                                          Name:  Walter T. Duffy III
                                          Title: Director



                                      By: /s/ PAUL VERDI
                                          --------------------------------
                                          Name:  Paul Verdi
                                          Title: Associate Director
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS BOOKRUNNER, AND
                                      NORDEA BANK FINLAND PLC, NEW YORK BRANCH,
                                      AS ADMINISTRATIVE AGENT.

                                      NAME OF INSTITUTION:

                                      Southwest Bank of Texas N.A.


                                      By: /s/ C. ROSS BARTLEY
                                          --------------------------------
                                          Name:  C. Ross Bartley
                                          Title: Vice President
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS BOOKRUNNER, AND
                                      NORDEA BANK FINLAND PLC, NEW YORK BRANCH,
                                      AS ADMINISTRATIVE AGENT.

                                      NAME OF INSTITUTION:

                                      DnB NOR Bank ASA, New York Branch


                                      By: /s/ NIKOLAI A. NACHAMKIN
                                          --------------------------------
                                          Name:  Nikolai A. Nachamkin
                                          Title: Senior Vice President


                                      By: /s/ SANJIV NAYAR
                                          --------------------------------
                                          Name:  Sanjiv Nayar
                                          Title: Senior Vice President
<PAGE>
                                      SIGNATURE PAGE TO THE SECOND AMENDMENT,
                                      DATED AS OF NOVEMBER 24, 2004, AMONG NOBLE
                                      CORPORATION, NOBLE HOLDING (U.S.)
                                      CORPORATION, NOBLE DRILLING CORPORATION,
                                      VARIOUS LENDERS PARTY TO THE CREDIT
                                      AGREEMENT, WELLS FARGO BANK, N.A. AND
                                      SUNTRUST BANK, AS DOCUMENTATION AGENTS,
                                      THE BANK OF TOKYO-MITSUBISHI, LTD. AND
                                      WESTDEUTSCHE LANDESBANK GIROZENTRALE, NEW
                                      YORK BRANCH, AS SYNDICATION AGENTS, THE
                                      BANK OF TOKYO-MITSUBISHI, LTD. AND NORDEA
                                      BANK FINLAND PLC, NEW YORK BRANCH, AS
                                      CO-LEAD ARRANGERS, NORDEA BANK FINLAND
                                      PLC, NEW YORK BRANCH, AS BOOKRUNNER, AND
                                      NORDEA BANK FINLAND PLC, NEW YORK BRANCH,
                                      AS ADMINISTRATIVE AGENT.

                                      NAME OF INSTITUTION:

                                      Barclays Bank PLC


                                      By: /s/ NICHOLAS BELL
                                          --------------------------------
                                          Name:  Nicholas Bell
                                          Title: Director
<PAGE>
                                                                         ANNEX I

                                   COMMITMENTS

<TABLE>
<CAPTION>
Lender                                                               Commitment
------                                                              ------------
<S>                                                                 <C>
Nordea Bank Norge ASA,
  Grand Cayman Branch                                               $ 50,000,000

The Bank of Tokyo-Mitsubishi, Ltd.                                  $ 50,000,000

SunTrust Bank                                                       $ 45,000,000

Wells Fargo Bank, N.A.                                              $ 45,000,000

Westdeutsche Landesbank Girozentrale,
  New York Branch                                                   $ 40,000,000

Southwest Bank of Texas, N.A.                                       $ 25,000,000

DnB NOR Bank ASA,
  New York Branch                                                   $ 25,000,000

Barclays Bank PLC                                                   $ 20,000,000
                                                                    ------------
TOTAL                                                               $300,000,000
                                                                    ============
</TABLE>