EOG RESOURCES, INC. 5.10% SENIOR NOTES DUE 2036

Exhibit 4.4

THIS SECURITY IS A GLOBAL SECURITY WITHIN THE MEANING OF THE INDENTURE HEREINAFTER REFERRED TO AND IS REGISTERED IN THE NAME OF THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION (“DTC”) OR CEDE & CO., ITS NOMINEE (“CEDE & CO.”). THIS SECURITY MAY NOT BE EXCHANGED IN WHOLE OR IN PART FOR A SECURITY REGISTERED, AND NO TRANSFER OF THIS SECURITY IN WHOLE OR IN PART MAY BE REGISTERED, IN THE NAME OF ANY PERSON OTHER THAN DTC OR CEDE & CO. OR ANOTHER NOMINEE OF DTC, EXCEPT IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE INDENTURE.

UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF DTC TO THE ISSUER OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT, AND ANY CERTIFICATE ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER NAME AS IS 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 THEREIN.

EOG RESOURCES, INC.

5.10% SENIOR NOTES DUE 2036

EOG Resources, Inc., a corporation duly organized and existing under the laws of Delaware (herein called the “Company,” which term includes any successor Person under the Indenture hereinafter referred to), for value received, hereby promises to pay to Cede & Co., as the nominee of The Depository Trust Company, or registered assigns, the principal sum of          DOLLARS AND          CENTS ($        ) on January 15, 2036 and to pay interest thereon from January 14, 2016 or from the most recent Interest Payment Date to which interest has been paid or duly provided for, semi-annually on January 15 and July 15 in each year (or if any such date is not a Business Day, the next succeeding Business Day), commencing July 15, 2016, at the rate of 5.10% per annum, until the principal hereof is paid or made available for payment.

The interest so payable, and punctually paid or duly provided for, on any Interest Payment Date will, as provided in such Indenture, be paid to the Person in whose name this Security (or one or more Predecessor Securities) is registered at the close of business on the Regular Record Date for such interest, which shall be January 1 or July 1 (whether or not a Business Day), as the case may be, next preceding such Interest Payment Date. Any such interest not so punctually paid or duly provided for will forthwith cease to be payable to the Holder on such Regular Record Date and may either be paid to the Person in whose name this Security (or one or more Predecessor Securities) is registered at the close of business on a Special Record Date for the payment of such Defaulted Interest to be fixed by the Trustee, notice whereof shall be given to Holders of Securities of this series not less than 10 days prior to such Special Record Date, or be paid at any time in any other lawful manner not inconsistent with the requirements of any securities exchange on which the Securities of this series may be listed, and upon such notice as may be required by such exchange, all as more fully provided in said Indenture. Payment of the principal of and interest on this Security will be made at the office or agency of the Company maintained for that purpose in Houston, Texas, in such coin or currency of the United States of America as at the time of payment is legal tender for payment of public and private debts; provided, however, that at the option of the Company payment of interest may be made by check mailed to the address of the Person entitled thereto as such address shall appear in the Security Register; provided, further, however, that in case this Security is held by a Depository or its nominee, payment of principal, interest and premium, if any, shall be made by wire transfer of immediately available funds to an account designated by such Depository.

Reference is hereby made to the further provisions of this Security set forth on the reverse hereof, which further provisions shall for all purposes have the same effect as if set forth at this place.

Unless the certificate of authentication hereon has been executed by the Trustee referred to on the reverse hereof by manual signature, this Security shall not be entitled to any benefit under the Indenture or be valid or obligatory for any purpose.

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IN WITNESS WHEREOF, the Company has caused this instrument to be duly executed under its corporate seal.

REVERSE OF SECURITY

This security is one of a duly authorized issue of securities of the Company (herein called the “Securities”) issued and to be issued in one or more series under an Indenture, dated as of May 18, 2009 (herein called the “Indenture”), between the Company and Wells Fargo Bank, National Association, as trustee (herein called the “Trustee,” which term includes any successor trustee under the Indenture), to which the Indenture and all indentures supplemental thereto (including as supplemented by an Officers’ Certificate pursuant thereto) reference is hereby made for a statement of the respective rights, limitations of rights, duties and immunities thereunder of the Company, the Trustee and the Holders of the Securities and of the terms upon which the Securities are, and are to be, authenticated and delivered. This Security is one of the series designated on the face hereof.

The Company may redeem some or all of the Securities of this series upon not less than 30 days’ notice by mail, at any time and from time to time prior to July 15, 2035, at the election of the Company, at a Redemption Price equal to the greater of a) 100% of the principal amount of the Securities then outstanding to be redeemed; or b) the sum of the present values of the remaining scheduled payments of principal and interest on the Securities to be redeemed (not including any portion of such payments of interest accrued 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 applicable Treasury Rate plus 35 basis points, plus, in each case, accrued and unpaid interest on the principal amount being redeemed to, but not including, the Redemption Date, but interest installments whose Stated Maturity is on or prior to such Redemption Date will be payable to the Holders of such Securities, or one or more Predecessor Securities, of record at the close of business on the relevant Record Dates referred to on the face hereof, all as provided in the Indenture.

The Company may redeem some or all of the Securities of this series upon not less than 30 days’ notice by mail, at any time and from time to time on or after July 15, 2035, at the election of the Company, at a Redemption Price equal to 100% of the principal amount of the Securities to be redeemed, plus accrued and unpaid interest on the principal amount being redeemed to, but not including, the Redemption Date.

In the event of redemption of this Security in part only, a new Security or Securities of this series and of like tenor for the unredeemed portion hereof will be issued in the name of the Holder hereof upon the cancellation hereof.

If an Event of Default with respect to Securities of this series shall occur and be continuing, the principal of the Securities of this series may be declared due and payable in the manner and with the effect provided in the Indenture.

The Indenture permits, with certain exceptions as therein provided, the amendment thereof and the modification of the rights and obligations of the Company and the rights of the Holders of the Securities of each series to be affected under the Indenture at any time by the Company and the Trustee with the consent of the Holders of more than 50% in principal amount of the Securities at the time Outstanding of each series to be affected. The Indenture also contains provisions permitting the Holders of specified percentages in principal amount of the Securities of each series

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at the time Outstanding, on behalf of the Holders of all Securities of such series, to waive compliance by the Company with certain provisions of the Indenture and certain past defaults under the Indenture and their consequences. Any such consent or waiver by the Holder of this Security shall be conclusive and binding upon such Holder and upon all future Holders of this Security and of any Security issued upon the registration of transfer hereof or in exchange herefor or in lieu hereof, whether or not notation of such consent or waiver is made upon this Security.

The Indenture contains provisions for defeasance at any time of the entire indebtedness of the Company on this Security upon compliance by the Company with certain conditions set forth therein, which provisions apply to this Security.

No reference herein to the Indenture and no provision of this Security or of the Indenture shall, without the consent of the Holder, alter or impair the right of the Holder, which is absolute and unconditional, to receive payment of principal of and any premium and interest on this Security at the times, place and rate, and in the coin or currency, herein prescribed, except for Section 113 of the Indenture (which limits interest to the maximum amount permissible by law), the provisions of which are incorporated herein by reference.

As provided in the Indenture and subject to certain limitations therein set forth, the transfer of this Security is registerable in the Security Register, upon surrender of this Security for registration of transfer at the office or agency of the Company in any place where the principal of and any premium and interest on this Security are payable, duly endorsed by, or accompanied by a written instrument of transfer in form satisfactory to the Company and the Security Registrar duly executed by, the Holder hereof or his attorney duly authorized in writing, and thereupon one or more new Securities of this series, of authorized denominations and for the same aggregate principal amount, will be issued to the designated transferee or transferees.

The Securities of this series are issuable only in registered form without coupons in denominations of $2,000 and integral multiples of $1,000 in excess thereof. As provided in the Indenture and subject to certain limitations therein set forth, Securities of this series are exchangeable for a like aggregate principal amount of Securities of this series of a different authorized denomination, as requested by the Holder surrendering the same.

No service charge shall be made for any such registration of transfer or exchange, but the Company may require payment of a sum sufficient to cover any tax or other governmental charge payable in connection therewith.

Prior to due presentment of this Security for registration of transfer, the Company, the Trustee and any agent of the Company or the Trustee may treat the Person in whose name this Security is registered as the owner hereof for all purposes, whether or not this Security be overdue, and neither the Company, the Trustee nor any such agent shall be affected by notice to the contrary.

All terms used in this Security which are defined in the Indenture shall have the meanings assigned to them in the Indenture (including as the Indenture is supplemented by the Officers’ Certificate, dated January 14, 2016, establishing the form and terms of the Securities of this series).

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This is one of the Securities of the series designated therein referred to in the within-mentioned Indenture.