<PAGE>

                                                                     EXHIBIT 4.1

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                             MURPHY OIL CORPORATION








                                       and








                                  SUNTRUST BANK
                                        Trustee






                             -----------------------

                          Second Supplemental Indenture

                             Dated as of May 2, 2002

                             -----------------------





        $350,000,000 aggregate principal amount of 6.375% Notes Due 2012


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                               TABLE OF CONTENTS*

                                                                           Page

PARTIES ..................................................................... 1
RECITALS:
Purpose of Second Supplemental Indenture .................................... 1
Form of Note, Face .......................................................... 2
Form of Trustee's Certificate of Authentication ............................. 4
Form of Note, Reverse ....................................................... 5
Compliance with Legal Requirements .......................................... 8
Consideration ............................................................... 9
PART I: CREATION AND AUTHORIZATION OF NOTES ................................. 9
PART II: SPECIAL PROVISIONS APPLICABLE TO THIS SERIES ....................... 9
TESTIMONIUM .................................................................10
SIGNATURES AND SEALS ........................................................10










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* The Table of Contents is not part of this Second Supplemental Indenture.


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     SECOND SUPPLEMENTAL INDENTURE, dated as of May 2, 2002, between Murphy Oil
Corporation, a Delaware corporation (hereinafter sometimes referred to as the
"Company"), and SUNTRUST BANK, a Georgia state banking corporation and the
successor in interest to SUNTRUST BANK, NASHVILLE, N.A. (hereinafter sometimes
referred to as the "Trustee").


                                WITNESSETH THAT:


     WHEREAS, the Company and the Trustee have entered into an Indenture (the
"Indenture") dated as of May 4, 1999 providing for the issuance of debt
securities in series; and

     WHEREAS, for its lawful corporate purposes, the Company desires to create
and authorize the series 6.375% Notes due May 1, 2012 (hereinafter referred to
as the "Notes") initially in an aggregate principal amount of Three Hundred
Fifty Million Dollars ($350,000,000), and to provide the terms and conditions
upon which the Notes are to be executed, registered, authenticated, issued and
delivered, the Company has duly authorized the execution and delivery of this
Supplemental Indenture; and

     WHEREAS, the Notes and the certificate of authentication to be borne by the
Notes are to be substantially in the following forms, respectively;

<PAGE>

                                 [FORM OF NOTE]

                                     [FACE]

     Unless this certificate is presented by an authorized representative of The
Depository Trust Company, a New York corporation ("DTC"), to the Company or its
agent for registration of transfer, exchange or payment, and any certificate
issued is registered in the name of Cede & Co. or such other name as requested
by an authorized representative of DTC (and any payment is made to Cede & Co. or
to such other entity as is requested by an authorized representative of DTC),
ANY TRANSFER, PLEDGE OR OTHER USE HEREOF FOR VALUE OR OTHERWISE BY OR TO ANY
PERSON IS WRONGFUL inasmuch as the registered owner hereof, Cede & Co., has an
interest herein.

     Unless and until it is exchanged in whole or in part for Securities in
definitive registered form, this Security may not be transferred except as a
whole by the Depositary to the nominee of the Depositary or by a nominee of the
Depositary to the Depositary or another nominee of the Depositary or by the
Depositary or any such nominee to a successor Depositary or a nominee of such
successor Depositary.


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  No.  1                                                      CUSIP #626717 AB 8
                                                              $350,000,000

                             MURPHY OIL CORPORATION

                              6.375% Note Due 2012

     Murphy Oil Corporation, a corporation duly organized and existing under the
laws of the State of Delaware (herein called the "Company"), for value received,
hereby promises to pay to Cede & Co. or registered assigns, the principal sum of
Three Hundred Fifty Million Dollars ($350,000,000) on May 1, 2012, at the office
or agency of the Company in the Borough of Manhattan, The City of New York, in
such coin or currency of the United States of America as at the time of payment
shall be legal tender for the payment of public and private debts, and to pay
interest, semiannually on May 1 and November 1 of each year, commencing November
1, 2002, on said principal sum at said office or agency, in like coin or
currency, at the rate per year specified in the title of this Note; provided,
that payment of interest may be made on any Note issued in definitive form, at
the option of the Company by check mailed to the address of the person entitled
thereto as such address shall appear on the Security register. Interest on the
Note will accrue from the most recent date to which interest has been paid, or
if no interest has been paid, from May 2, 2002. The interest so payable on any
May 1 or November 1 will, subject to certain exceptions provided in the
Indenture dated as of May 4, 1999 (herein called the "Indenture") referred to on
the reverse hereof, be paid to the person in whose name this Note (or one or
more predecessor Notes) is registered at the close of business on the April 15
or October 15 (whether or not a Business Day), as the case may be, next
preceding such May 1 or November 1. Reference is made to the further provisions
of this Note set forth on the reverse hereof. Such further provisions shall for
all purposes have the same effect as though fully set forth at this place.

     This Note shall not be valid or become obligatory for any purpose until the
certificate of authentication hereon shall have been executed by the Trustee
under the Indenture referred to on the reverse hereof by manual signature.


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     IN WITNESS WHEREOF, Murphy Oil Corporation has caused this instrument to be
duly executed.

                                    MURPHY OIL CORPORATION



                                    By
                                       -----------------------------------------



                                    By
                                      ------------------------------------------




                     TRUSTEE'S CERTIFICATE OF AUTHENTICATION


Dated: May 2, 2002

     This is one of the Securities designated herein and referred to in the
within-mentioned Indenture.


                                            SUNTRUST BANK
                                            as Authorized Signatory


                                            By:
                                                --------------------------------
                                                      Authorized Officer



                                       4

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                                [REVERSE OF NOTE]

                             MURPHY OIL CORPORATION
                              6.375% Note Due 2012

     This Note is one of a duly authorized issue of unsecured debentures, notes,
or other evidences of indebtedness of the Company (hereinafter called the
"Securities") of the series hereinafter specified, all issued or to be issued
under and pursuant to an indenture dated as of May 4, 1999 (herein called the
"Indenture"), duly executed and delivered by the Company to SunTrust Bank, as
Trustee (herein called the "Trustee"), to which Indenture and all indentures
supplemental thereto reference is hereby made for a description of the rights,
limitations of rights, obligations, duties and immunities thereunder of the
Trustee, the Company and the Holders of the Securities. The Securities may be
issued in one or more series, which different series may be issued in various
aggregate principal amounts, may mature at different times, may bear interest
(if any) at different rates, may be subject to different redemption provisions
(if any), may be subject to different sinking, purchase or analogous funds (if
any) and may otherwise vary as provided in the Indenture. This Note is one of a
series designated as the 6.375% Notes Due 2012 (the "Notes") of the Company,
initially limited in aggregate principal amount to $350,000,000.

     In case an Event of Default with respect to the Notes shall have occurred
and be continuing, the principal hereof may be declared, and upon such
declaration shall become, due and payable, in the manner, with the effect and
subject to the conditions provided in the Indenture.

     The Indenture contains provisions permitting the Company and the Trustee,
with the consent of the Holders of not less than a majority in aggregate
principal amount of the Securities of each series issued under such Indenture
then Outstanding and affected, to add any provisions to, or change in any manner
or eliminate any of the provisions of, such Indenture or modify in any manner
the rights of the Holders of the Securities of each series so affected; provided
that the Company and the Trustee may not, without the consent of the Holder of
each outstanding Security affected thereby, (i) extend the stated maturity of
any Security, or reduce the principal amount thereof or reduce the rate or
extend the time of payment of interest thereon, or reduce any amount payable on
redemption thereof or reduce the principal amount of any original issue discount
security payable upon acceleration or provable in bankruptcy or impair or affect
the right to institute suit for the payment on any Security when due or (ii)
reduce the aforesaid percentage in aggregate principal amount of Securities of
any series issued under such Indenture, the consent of the Holders of which is
required for any such modification. It is also provided in the Indenture that,
with respect to


                                       5

<PAGE>

certain defaults or Events of Default regarding the Securities of any series,
prior to any declaration accelerating the maturity of such Securities, the
Holders of a majority in aggregate principal amount Outstanding of the
Securities of such series (or, in the case of certain defaults or Events of
Default, all or certain series of the Securities) may on behalf of the Holders
of all the Securities of such series (or, in the case of certain defaults or
Events of Default, all or certain series of the Securities, as the case may be)
waive any such past default or Event of Default and its consequences. The
preceding sentence shall not, however, apply to a default in the payment of the
principal of or interest on any of the Securities. Any such consent or waiver by
the Holder of this Note (unless revoked as provided in the Indenture) shall be
conclusive and binding upon such Holder and upon all future Holders and owners
of this Note and any Notes which may be issued in exchange or substitution
herefor or on registration of transfer hereof, irrespective of whether or not
any notation thereof is made upon this Note or such other Notes.

     The Company may from time to time, without the consent of the Outstanding
Holders, create and issue additional Notes having the same terms and conditions
as the 6.375% Notes due 2012, except for the issue date, issue price and, under
some circumstances, the date of the first payment of interest on the notes.
Additional Notes issued in this manner will be consolidated with and form a
single series with the 6.375% Notes due 2012. No reference herein to the
Indenture and no provision of this Note or of the Indenture shall alter or
impair the obligation of the Company, which is absolute and unconditional, to
pay the principal of and interest on this Note in the manner, at the respective
times, at the rate and in the coin or currency herein prescribed.

     The Notes are redeemable as a whole or in part, at the option of the
Company at any time and from time to time, at a "make-whole" redemption price
equal to the greater of (i) 100% of principal amount of such Notes, or (ii) the
sum of the present values of the Remaining Scheduled Payments of the Notes being
redeemed (exclusive of any accrued and unpaid interest to the redemption date),
discounted to the redemption date on a semiannual basis (assuming a 360-day year
consisting of twelve 30-day months) at the Treasury Rate plus 25 basis points,
plus in each case accrued interest thereon, if any, to the date of redemption.

     "Comparable Treasury Issue" means the United States Treasury security
selected by an Independent Investment Banker that would be used, at the time of
selection and in accordance with customary financial practice, in pricing new
issues of corporate debt securities of comparable maturity to the remaining term
of the Notes.


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<PAGE>

     "Comparable Treasury Price" means:

     .    the average of the bid and asked prices for the Comparable Treasury
          Issue (expressed in each case as a percentage of its principal amount)
          as of the third business day preceding the redemption date, as set
          forth in the daily statistical release (or any successor release)
          published by the Federal Reserve Bank of New York and designated
          "Composite 3:30 p.m. Quotations for U.S. Government Securities," or

     .    if that release (or any successor release) is not published or does
          not contain such prices on that business day, (a) the average of the
          Reference Treasury Dealer Quotations for the redemption date, after
          excluding the highest and lowest of such Reference Treasury Dealer
          Quotations, or (b) if the Trustee obtains fewer than four such
          Reference Treasury Dealer Quotations, the average of all quotations
          obtained.

     "Independent Investment Banker" means one of the Reference Treasury Dealers
that the Company appoints.

     "Reference Treasury Dealer" means each of Banc of America Securities LLC
and J.P. Morgan Securities Inc. (and their respective successors) and three
other nationally recognized investment banking firms that are primary U.S.
Government securities dealers specified from time to time by the Company. If,
however, any of them shall cease to be a primary U.S. Government securities
dealer, the Company will substitute another nationally recognized investment
banking firm that is such a dealer.

     "Reference Treasury Dealer Quotations" means, with respect to each
Reference Treasury Dealer and any redemption date, the average, as determined by
the Trustee, of the bid and asked prices for the Comparable Treasury Issue
(expressed in each case as a percentage of its principal amount) quoted in
writing to the Trustee by such Reference Treasury Dealer as of 3:30 p.m., New
York time, on the third business day preceding the redemption date.

     "Remaining Scheduled Payments" means the remaining scheduled payments of
the principal of and interest on each Note to be redeemed that would be due
after the related redemption date but for such redemption. If the redemption
date is not an interest payment date with respect to the Note being redeemed,
the amount of the next succeeding scheduled interest payment on the Note will be
reduced by the amount of interest accrued thereon to that redemption date.


                                       7

<PAGE>

     "Treasury Rate" means the rate per year equal to the semiannual equivalent
yield to maturity (computed as of the second business day immediately preceding
the redemption date) of the Comparable Treasury Issue, assuming a price for the
Comparable Treasury Issue (expressed as a percentage of its principal amount)
equal to the Comparable Treasury Price for the redemption date.

     The Notes are issuable in fully registered form, without coupons, in
denominations of $1,000 and any integral multiple of $1,000 at the office or
agency of the Company in the Borough of Manhattan, The City of New York, and in
the manner and subject to the limitations provided in the Indenture, but without
the payment of any service charge. Notes may be exchanged for a like aggregate
principal amount of Notes of other authorized denominations.

     Upon due presentment for registration of transfer of this Note at the
office or agency of the Company in the Borough of Manhattan, The City of New
York, a new Note or Notes of authorized denominations for an equal aggregate
principal amount will be issued to the transferee in exchange therefor, subject
to the limitations provided in the Indenture, without charge except for any tax
or other governmental charge imposed in connection therewith.

     The Company, the Trustee and any authorized agent of the Company or the
Trustee may deem and treat the registered Holder hereof as the absolute owner of
this Note (whether or not this Note shall be overdue and notwithstanding any
notation of ownership or other writing hereon), for the purpose of receiving
payment of, or on account of, the principal hereof and subject to the provisions
on the face hereof, interest hereon, and for all other purposes, and none of the
Company, the Trustee or any authorized agent of the Company or the Trustee shall
be affected by any notice to the contrary.

     No recourse under or upon any obligation, covenant or agreement of the
Company in the Indenture or any indenture supplemental thereto or in any Note,
or because of the creation of any indebtedness represented thereby, shall be had
against any incorporator, stockholder, officer or director, as such of the
Company or of any successor corporation, either directly or through the Company
or any successor corporation, under any rule of law, statute or constitutional
provision or by the enforcement of any assessment or by any legal or equitable
proceeding or otherwise, all such liability being expressly waived and released
by the acceptance hereof and as part of the consideration for the issue hereof.

     This Note shall for all purposes be governed by, and construed in
accordance with, the laws of the State of New York.

     Terms used herein which are defined in the Indenture shall have the
respective meanings assigned thereto in the Indenture.


                                       8

<PAGE>

     AND WHEREAS, all acts and things necessary to make the Notes, when executed
by the Company and authenticated and delivered by or on behalf of the Trustee as
in this Indenture provided, the valid, binding and legal obligations of the
Company, and to constitute these presents a valid Indenture and agreement
according to its terms, have been done and performed.

     NOW THEREFORE:

     In order to declare the terms and conditions upon which the Notes are
executed, registered, authenticated, issued and delivered, and in consideration
of the premises, of the purchase and acceptance of such Notes by the holders
thereof and of the sum of one dollar to it duly paid by the Trustee at the
declaration of these presents, the receipt whereof is hereby acknowledged, the
Company covenants and agrees with the Trustee, for the equal and proportionate
benefit of the respective holders from time to time by such Notes, as follows:


                                     PART I

                       CREATION AND AUTHORIZATION OF NOTES

     There is hereby created and authorized the series of Notes entitled the
"6.375% Notes Due 2012", which shall be a series initially limited to
$350,000,000 aggregate principal amount (except such Notes authenticated and
delivered upon registration of transfer of, or in exchange for, or in lieu of,
other Notes of this series pursuant to Sections 2.08, 209, 2.11 or 11.03 of the
Indenture).

                                    PART II

                  SPECIAL PROVISIONS APPLICABLE TO THIS SERIES

     There are no special provisions applicable to this Series.


                                       9

<PAGE>

     IN WITNESS WHEREOF, Murphy Oil Corporation has caused this Second
Supplemental Indenture to be signed and delivered and its corporate seal to be
affixed hereunto and the same to be attested, and the Trustee has caused this
Second Supplemental Indenture to be signed and delivered and its corporate seal
to be affixed hereunto and the same to be attested, all as of the day and year
first written above.



                                    MURPHY OIL CORPORATION


                                    By /s/ Kevin G. Fitzgerald
                                      ------------------------------------------


                                    [CORPORATE SEAL]
                                    ATTEST:

                                       /s/ Walter K. Compton
                                    --------------------------------------------





                                    SUNTRUST BANK
                                    AS TRUSTEE

                                    By  /s/ Vincent R. Harrison
                                      ------------------------------------------


                                    [CORPORATE SEAL]
                                    ATTEST:

                                        /s/ Donna L. Williams
                                    --------------------------------------------


                                       10