<PAGE>
                                                                     EXHIBIT 4.2


                               FIRST AMENDMENT
                                      TO
                               RIGHTS AGREEMENT


         This First Amendment to Rights Agreement, made effective as of the
12th day of March, 2003, amends that certain Rights Agreement, dated as of March
13, 2002 (the "Rights Agreement"), between Noble Corporation, a Cayman Islands
exempted company limited by shares (the "Company"), and UMB Bank, N.A., as
Rights Agent (the "Rights Agent").

         WHEREAS, Section 27 of the Rights Agreement provides in part that prior
to the "Distribution Date" (as defined in the Rights Agreement), and subject to
the last sentence of Section 27, the Board of Directors of the Company and the
Rights Agent may amend any provision of the Rights Agreement in any manner; and

         WHEREAS, on January 31, 2003, the Board of Directors of the Company
approved an amendment of the Rights Agreement to increase from 15% to 25% the
maximum percentage of the outstanding Ordinary Shares, par value US$.10, of the
Company that any Person, and such Person's Affiliates and Associates (as such
terms are defined in the Rights Agreement), could beneficially own without
causing the Rights to become exercisable;

         NOW THEREFORE, the Rights Agreement is hereby amended as follows:

         1. The definition of "ACQUIRING PERSON" contained in Section 1 of the
Rights Agreement is hereby amended to read in its entirety as follows:

                  "'ACQUIRING PERSON' shall mean any Person (as such term is
         hereinafter defined) who or which, together with all Affiliates and
         Associates (as such terms are hereinafter defined) of such Person,
         shall be the Beneficial Owner (as such term is hereinafter defined) of
         25 percent or more of the Ordinary Shares of the Company then
         outstanding, but shall not include the Company, any Subsidiary (as such
         term is hereinafter defined) of the Company, any employee benefit plan
         of the Company or any Subsidiary of the Company, or any entity holding
         Ordinary Shares of the Company for or pursuant to the terms of any such
         plan. Notwithstanding the foregoing, no Person shall become an
         'Acquiring Person' as the result of an acquisition of Ordinary Shares
         of the Company by the Company which, by reducing the number of such
         shares outstanding, increases the proportionate number of shares
         beneficially owned by such Person to 25 percent or more of the Ordinary
         Shares of the Company then outstanding; provided, however, that if a
         Person shall become the Beneficial Owner of 25 percent or more of the
         Ordinary Shares of the Company then outstanding by reason of share
         purchases by the Company and shall, after such share purchases by the
         Company, become the Beneficial Owner of any additional Ordinary Shares
         of the Company, then such Person shall be deemed to be an 'Acquiring
         Person.' Notwithstanding the foregoing, if the Board of Directors of
         the Company determines in good faith that a Person who would otherwise
         be an 'Acquiring Person,' as defined pursuant to the foregoing
         provisions of this definition, has become such inadvertently, and such
         Person divests as promptly as practicable a sufficient number of
         Ordinary Shares of the Company so that such Person would no longer be
         an


                                        1
<PAGE>

         'Acquiring Person,' as defined pursuant to the foregoing provisions of
         this definition, then such person shall not be deemed to be an
         'Acquiring Person' for any purposes of this Agreement."

         2. Section 3(b) of the Rights Agreement is hereby amended in its
entirety to read as follows:

                  "(b) Until the earlier of (i) the tenth day after the Shares
         Acquisition Date and (ii) the tenth Business Day (or such later date as
         may be determined by action of the Board of Directors of the Company
         prior to such time as any Person becomes an Acquiring Person) after the
         date of the commencement by any Person (other than the Company, any
         Subsidiary of the Company, any employee benefit plan of the Company or
         any Subsidiary of the Company, or any entity holding Ordinary Shares of
         the Company for or pursuant to the terms of any such plan) of, or of
         the first public announcement of the intention of any Person (other
         than the Company, any Subsidiary of the Company, any employee benefit
         plan of the Company or any Subsidiary of the Company, or any entity
         holding Ordinary Shares of the Company for or pursuant to the terms of
         any such plan) to commence, a tender or exchange offer the consummation
         of which would result in any Person becoming the Beneficial Owner of
         Ordinary Shares aggregating 25 percent or more of the then outstanding
         Ordinary Shares (including any such date which is after the date of
         this Agreement and prior to the issuance of the Rights; the earlier of
         such dates being herein referred to as the 'Distribution Date'), (x)
         the Rights will be evidenced (subject to the provisions of Section 3(c)
         hereof) by the certificates for Ordinary Shares registered in the names
         of the holders thereof (which certificates shall also be deemed to be
         Right Certificates) and not by separate Right Certificates, and (y) the
         Rights, including the right to receive Right Certificates, will be
         transferable only in connection with the transfer of Ordinary Shares.
         As soon as practicable after the Distribution Date, the Company will
         prepare and execute, the Rights Agent will countersign, and the Company
         will send or cause to be sent (and the Rights Agent will, if requested,
         send) by first-class, insured, postage-prepaid mail, to each record
         holder of Ordinary Shares as of the close of business on the
         Distribution Date, at the address of such holder shown on the records
         of the Company, a Right Certificate evidencing one whole Right for each
         Ordinary Share (or for the number of Ordinary Shares with which one
         whole Right is then associated if the number of Rights per Ordinary
         Share held by such record holder has been adjusted in accordance with
         the provision in Section 3(a) hereof) so held. If the number of Rights
         associated with each Ordinary Share has been adjusted in accordance
         with the proviso in Section 3(a) hereof, at the time of distribution of
         the Right Certificates, the Company may make any necessary and
         appropriate rounding adjustments so that Right Certificates
         representing only whole numbers of Rights are distributed and cash is
         paid in lieu of any fractional Right in accordance with Section 14
         hereof. As of and after the Distribution Date, the Rights will be
         evidenced solely by such Right Certificates."


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


                                        2
<PAGE>
         IN WITNESS WHEREOF, the Company and the Rights Agent have duly executed
this First Amendment to Rights Agreement effective as of the date first written
above.

                                         THE "COMPANY"
                                         NOBLE CORPORATION


                                         By: /s/ ROBERT D. CAMPBELL
                                            ------------------------------------
                                         Name:  Robert D. Campbell
                                              ----------------------------------
                                         Title: President
                                               ---------------------------------


                                         THE "RIGHTS AGENT"
                                         UMB BANK, N.A.


                                         By: /s/ R. WILLIAM BLOEMKER
                                            ------------------------------------
                                         Name:  R. William Bloemker
                                              ----------------------------------
                                         Title: Vice President
                                               ---------------------------------


                                        3