MURPHY OIL CORPORATION as Issuer and U.S. BANK NATIONAL ASSOCIATION as Trustee First Supplemental Indenture Dated as of May 18, 2012 $500,000,000 aggregate principal amount of 4.00% Notes Due 2022

Exhibit 4.2

EXECUTION COPY

MURPHY OIL CORPORATION

as Issuer

and

U.S. BANK NATIONAL ASSOCIATION

as Trustee

First Supplemental Indenture

Dated as of May 18, 2012

$500,000,000 aggregate principal amount of 4.00% Notes Due 2022

FIRST SUPPLEMENTAL INDENTURE (this “Supplemental Indenture”), dated as of May 18, 2012, between MURPHY OIL CORPORATION, a Delaware corporation (the “Issuer”), and U.S. BANK NATIONAL ASSOCIATION, as Trustee (the “Trustee”).

WITNESSETH THAT:

WHEREAS, the Issuer and the Trustee have entered into an Indenture (the “Base Indenture” and, as supplemented by this Supplemental Indenture, the “Indenture”) dated as of May 18, 2012 providing for the issuance from time to time of series of its Securities (as defined in the Base Indenture); and

WHEREAS, Section 7.01(e) of the Base Indenture provides for the Issuer and the Trustee to enter into an indenture supplemental to the Base Indenture to establish the form or terms of Securities of any series as permitted by Sections 2.01 and 2.03 of the Base Indenture; and

WHEREAS, pursuant to Section 2.03 of the Base Indenture, the Issuer, for its lawful corporate purposes, desires to create and authorize a new series of Securities to be known as the 4.00% Notes Due 2022 (the “Notes”), initially in an aggregate principal amount of Five Hundred Million Dollars ($500,000,000), and to be due June 1, 2022; and

WHEREAS, the Issuer has duly authorized the execution and delivery of this Supplemental Indenture, which sets forth the terms and conditions upon which the Notes are to be executed, registered, authenticated, issued and delivered; and

WHEREAS, all things necessary to make this Supplemental Indenture a valid agreement according to its terms have been done, and all things necessary to make the Notes, when executed by the Issuer and authenticated and delivered by or on behalf of the Trustee as in this Supplemental Indenture provided, the valid, binding and legal obligations of the Issuer have been done;

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 for other good and valuable consideration, the receipt and sufficiency of which is hereby acknowledged, the Issuer covenants and agrees with the Trustee, for the equal and proportionate benefit of the respective holders from time to time of such Notes, as follows:

ARTICLE 1

DEFINITIONS

Section 1.01. Relation to Base Indenture. This Supplemental Indenture constitutes an integral part of the Base Indenture. However, to the extent any provision of the Base Indenture conflicts with the express provisions of this Supplemental Indenture, the provisions of this Supplemental Indenture will govern and be controlling in respect of the Notes.

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Section 1.02. Definition of Terms. For all purposes of this Supplemental Indenture:

(a) capitalized terms used herein without definition shall have the meanings specified in the Base Indenture; and

(b) the following terms (except as otherwise expressly provided or unless the context otherwise clearly requires) shall have the respective meanings as set forth in this Section 1.02:

“Comparable Treasury Issue” means the U.S. Treasury security selected by an Independent Investment Banker as having a maturity comparable to the remaining term (“Remaining Life”) of the Notes to be redeemed that would be utilized, 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 such Notes.

“Comparable Treasury Price” means (i) the average of four Reference Treasury Dealer Quotations for the relevant date fixed for redemption, after excluding the highest and lowest Reference Treasury Dealer Quotations, or (ii) if the Independent Investment Banker obtains fewer than four such Reference Treasury Dealer Quotations, the average of all such quotations.

“Independent Investment Banker” means one of J.P. Morgan Securities LLC and Wells Fargo Securities, LLC, or their respective successors, as specified by the Issuer, or, if those firms are unwilling or unable to select the Comparable Treasury Issue, an independent investment banking institution of national standing appointed by the Issuer.

“Reference Treasury Dealer” means each of (i) J.P. Morgan Securities LLC and Wells Fargo Securities, LLC, or their respective successors, provided, however, that if any of the foregoing shall cease to be a primary U.S. government securities dealer in the United States (a “Primary Treasury Dealer”), the Issuer will substitute therefor another Primary Treasury Dealer and (ii) any two other Primary Treasury Dealers selected by the Issuer after consultation with an Independent Investment Banker.

“Reference Treasury Dealer Quotations” means, with respect to each Reference Treasury Dealer and any date fixed for redemption, the average, as determined by the Independent Investment Banker, of the bid and ask prices for the Comparable Treasury Issue (expressed in each case as a percentage of its principal amount) quoted in writing to the Independent Investment Banker at 5:00 p.m., New York City time, on the Calculation 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 date fixed for redemption but for such redemption. If the date fixed for redemption 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 date fixed for redemption.

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“Treasury Rate” means, with respect to any date fixed for redemption, (i) the yield, under the heading which represents the average for the immediately preceding week, appearing in the most recently published statistical release designated “H.15(519)” or any successor publication which is published weekly by the Board of Governors of the Federal Reserve System and which establishes yields on actively traded U.S. Treasury securities adjusted to constant maturity under the caption “Treasury Constant Maturities,” for the maturity corresponding to the Comparable Treasury Issue (if no maturity is within three months before or after the Remaining Life, yields for the two published maturities most closely corresponding to the Comparable Treasury Issue will be determined and the Treasury Rate will be interpolated or extrapolated from such yields on a straight line basis, rounding to the nearest month); or (ii) if such release (or any successor release) is not published during the week preceding the Calculation Date or does not contain such yields, the rate per annum equal to the semi-annual equivalent yield to maturity of the Comparable Treasury Issue, calculated using a price for the Comparable Treasury Issue (expressed as a percentage of its principal amount) equal to the Comparable Treasury Price for such date fixed for redemption. The Treasury Rate will be calculated on the third business day next preceding the date fixed for redemption (the “Calculation Date”).

The terms “Supplemental Indenture,” “Issuer,” “Trustee,” “Indenture,” “Base Indenture” and “Notes” shall have the respective meanings set forth in the recitals to this Supplemental Indenture and the paragraph preceding such recitals.

ARTICLE 2

GENERAL TERMS AND CONDITIONS OF THE NOTES

Section 2.01. Designation and Principal Amount. There is hereby created and authorized a series of Notes designated as the “4.00% Notes Due 2022”, which shall be a series initially limited to $500,000,000 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, 2.09, 2.11 or 11.03 of the Base Indenture) and which shall be initially due on June 1, 2022.

Section 2.02. Form of Notes. The Notes and the Trustee’s certificate of authentication to be borne by the Notes are to be substantially in the forms attached as Exhibit A hereto, with such appropriate insertions, omissions, substitutions and other variations as are required or permitted by the Indenture and may have imprinted or otherwise reproduced thereon such legend or

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legends, not inconsistent with the provisions of the Indenture, as may be required to comply with any law or with any rules or regulations pursuant thereto, or with any rules of any securities exchange or to conform to general usage, all as may be determined by the officers executing such Notes, as evidenced by their execution of the Notes. The Notes shall be initially issued in the form of one or more Global Securities in denominations of $2,000 and any integral multiple of $1,000 in excess thereof at the office or agency of the Issuer in the Borough of Manhattan, The City of New York, and in the manner and subject to the limitations provided in the Base Indenture, but without the payment of any service charge.

Section 2.03. Additional Notes. The Issuer may from time to time, without the consent of the existing Holders and notwithstanding Section 2.01 of this Supplemental Indenture, create and issue additional Notes hereunder having the same terms and conditions as the Notes initially issued hereunder in all respects, except for the issue date, issue price and the date of the first payment of interest on any such additional Notes (if such additional Notes are issued after the first interest payment date immediately following the date of this Supplemental Indenture); provided that if any such additional Notes are not fungible with the Notes initially issued hereunder for U.S. federal income tax purposes, such additional Notes shall have a different CUSIP number. Additional Notes issued pursuant to this Section 2.03 shall be consolidated with and form a single series with the previously outstanding Notes.

ARTICLE 3

REDEMPTION OF THE NOTES

Section 3.01. Optional Redemption. The Issuer may redeem the Notes in accordance with Article 11 of the Base Indenture as a whole at any time or in part from time to time, at its option, at a redemption price (the “Redemption Price”) equal to:

(a) if the date fixed for redemption for the Notes being redeemed is prior to March 1, 2022, 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 principal and interest on the Notes to be redeemed, discounted to the date fixed for redemption on a semi-annual basis (assuming a 360-day year consisting of twelve 30-day months) at the Treasury Rate plus 35 basis points,

plus, in either case, accrued and unpaid interest on the principal amount of the Notes being redeemed to, but not including, the date fixed for redemption, or

(b) if the date fixed for redemption for the Notes being redeemed is on or after March 1, 2022, 100% of the principal amount of such Notes, plus accrued and unpaid interest on the principal amount of such Notes to, but not including, the date fixed for redemption.

The Redemption Price pursuant to clause (a) shall be calculated by the Independent Investment Banker and the Issuer, the Trustee and any Paying Agent for the Notes shall be entitled to rely on such calculation.

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Section 3.02. No Other Redemption. Except as set forth in this Article 3 and Article 11 of the Base Indenture, the Notes shall not be redeemable by the Issuer prior to maturity and shall not be entitled to the benefit of any sinking fund. For the avoidance of doubt, Section 11.05 of the Base Indenture shall not apply to the Notes.

ARTICLE 4

EVENTS OF DEFAULT

Section 4.01. Automatic Acceleration. If an Event of Default occurs pursuant to clause (e) or clause (f) of the definition thereof in Section 4.01 of the Base Indenture, then, notwithstanding anything to the contrary in the Indenture, the principal amount of and accrued interest on the Notes shall be immediately due and payable without any declaration or other act by the Trustee or any Holder.

Section 4.02. Certificated Notes. If an Event of Default has occurred and is continuing, and the Depositary requests the issuance of Notes in definitive registered form, then the Issuer shall execute, and the Trustee, upon receipt of an Issuer Order for the authentication and delivery of definitive Notes, will authenticate and deliver, Notes in definitive registered form without coupons, in any authorized denominations, in an aggregate principal amount equal to the principal amount of the Global Security or Global Securities representing such Notes, in exchange for such Global Security or Global Securities.

ARTICLE 5

MISCELLANEOUS PROVISIONS

Section 5.01. Consolidation, Merger, Sale or Conveyance. For the avoidance of doubt, the sale or conveyance of that portion of the Issuer’s (and its Subsidiaries’) business consisting primarily of its retail and wholesale fuel marketing operations and two ethanol production facilities shall be deemed not to involve the sale or conveyance of all or substantially all of its assets within the meaning of Section 8.01 of the Base Indenture.

Section 5.02. Ratification of Indenture. The Base Indenture, as supplemented by this Supplemental Indenture, is in all respects ratified and confirmed, and this Supplemental Indenture shall be deemed to be part of the Base Indenture in the manner and to the extent herein and therein provided.

Section 5.03. New York Law to Govern. This Supplemental Indenture and each Note shall be deemed to be a contract under the laws of the State of New York, and for all purposes shall be construed in accordance with the laws of such State, without regard to conflicts of laws principles thereof, except as may otherwise be required by mandatory provisions of law.

Section 5.04. Counterparts. This Supplemental Indenture may be executed in any number of counterparts, each of which shall be an original; but such counterparts shall together constitute but one and the same instrument.

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Section 5.05. Effect of Headings. The Article and Section headings herein are for convenience only and shall not affect the construction hereof.

Section 5.06. Separability Clause. In case any provision of this Supplemental Indenture or in the Notes shall be invalid, illegal or unenforceable, the validity, legality and enforceability of the remaining provisions shall not in any way be affected or impaired thereby.

Section 5.07. Successors. All agreements of the Company in this Supplemental Indenture and the Notes will bind its successors. All agreements of the Trustee in this Supplemental Indenture will bind its successors.

[Remainder of Page Intentionally Blank]

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed as of the day and year first written above.

[Signature page to the First Supplement Indenture]

EXHIBIT A

[FORM OF FACE OF NOTE]

[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 SUCH DEPOSITARY OR BY THE DEPOSITARY OR ANY SUCH NOMINEE TO A SUCCESSOR DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITARY.]¹

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No. [__]

CUSIP No. 626717AD4

$[            ]

MURPHY OIL CORPORATION

4.00% Notes Due 2022

MURPHY OIL CORPORATION, a corporation duly organized and existing under the laws of the State of Delaware (the “Issuer”), for value received, hereby promises to pay to [            ] [CEDE & CO.]² or registered assigns, the principal sum of [            ] DOLLARS ($[            ]) [as revised on the Schedule of Exchanges of Notes attached hereto]³ on June 1, 2022, at the office or agency of the Issuer 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 June 1 and December 1 of each year, commencing December 1, 2012, 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 Issuer 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 18, 2012. The interest so payable on any June 1 or December 1 will, subject to certain exceptions provided in 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 May 15 or November 15 (whether or not a Business Day), as the case may be, next preceding such June 1 or December 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.

[Remainder of Page Intentionally Blank]

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

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TRUSTEE’S CERTIFICATE OF AUTHENTICATION

Dated: [            ], 20[__]

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

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[FORM OF REVERSE OF NOTE]

MURPHY OIL CORPORATION

4.00% Notes Due 2022

This Note is one of a duly authorized issue of unsecured debentures, notes, or other evidences of indebtedness of the Issuer (the “Securities”) of the series hereinafter specified, all issued or to be issued under and pursuant to an indenture dated as of May 18, 2012, as supplemented by the First Supplemental Indenture dated as of May 18, 2012 (as so supplemented, the “Indenture”), duly executed and delivered by the Issuer to U.S. Bank National Association, as Trustee (herein called the “Trustee”), to which Indenture and all other 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 Issuer 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 4.00% Notes Due 2022 (the “Notes”) of the Issuer, initially limited in aggregate principal amount to $500,000,000.

The Indenture contains provisions permitting the Issuer and the Trustee in certain circumstances, without the consent of the Holders of the Notes, and in certain other circumstances, with the consent of the Holders of not less than a majority in aggregate principal amount of the Notes at the time outstanding, evidenced as in the Indenture provided, to execute supplemental indentures modifying the terms of the Indenture and the Notes as described therein. It is also provided in the Indenture that, subject to certain exceptions, the Holders of a majority in aggregate principal amount of the Notes at the time outstanding may on behalf of the Holders of all of the Notes waive any past default or Event of Default under the Indenture and its consequences.

No reference herein to the Indenture and no provision of this Note or of the Indenture shall alter or impair the obligation of the Issuer, 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 at any time or in part from time to time, at the option of the Issuer, as set forth in the Indenture.

Upon due presentment for registration of transfer of this Note at the office or agency of the Issuer 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 Issuer, the Trustee and any authorized agent of the Issuer 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),

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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 Issuer, the Trustee or any authorized agent of the Issuer or the Trustee shall be affected by any notice to the contrary.

This Note shall for all purposes be governed by, and construed in accordance with, the laws of the State of New York, without regard to conflicts of laws principles thereof, except as may otherwise be required by mandatory provisions of law.

In the case of any conflict between this Note and the Indenture, the provisions of the Indenture shall control and govern.

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

[Remainder of Page Intentionally Blank]

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SCHEDULE A⁴

SCHEDULE OF EXCHANGES OF NOTES

MURPHY OIL CORPORATION 4.00% Notes Due 2022

The initial principal amount of this Global Security is [            ] DOLLARS ($[            ]). The following increases or decreases in this Global Security have been made:

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