FIFTH SUPPLEMENTAL INDENTURE

Exhibit 4.12

FIFTH SUPPLEMENTAL INDENTURE

This Fifth Supplemental Indenture (this “Supplemental Indenture”), dated as of May 3, 2011, is entered into by and among Southwest Airlines Co., a Texas corporation (“Southwest” or the “Successor Company”), and U.S. Bank National Association, a national banking association, as trustee hereunder (the “Trustee”). Capitalized terms used herein and not otherwise defined have the meanings set forth in the Indenture (as defined below).

WHEREAS, AirTran Holdings, Inc., a Nevada corporation (“AirTran Holdings Inc”), and the Trustee were the original parties to a Senior Indenture dated as of October 14, 2009 (the “Base Indenture”) and a First Supplemental Indenture dated as of October 14, 2009 relating to the issuance of the 5.25% Convertible Senior Notes due 2016 (the “First Supplemental Indenture”);

WHEREAS, AirTran Holdings Inc, Southwest and the Trustee were the original parties to a Second Supplemental Indenture dated as of May 2, 2011, which supplements the Base Indenture and the First Supplemental Indenture (the “Second Supplemental Indenture”), pursuant to which Second Supplemental Indenture (among other things) Southwest fully and unconditionally guaranteed the obligations of AirTran Holdings Inc, its wholly owned subsidiary, under the Indenture, under the Indenture and Securities;

WHEREAS, Southwest, AirTran Holdings, LLC, a Texas limited liability company (“AirTran LLC”), and the Trustee were the original parties to a Third Supplemental Indenture dated as of May 2, 2011, which supplements the Base Indenture, the First Supplemental Indenture and the Second Supplemental Indenture (the “Third Supplemental Indenture”), pursuant to which Third Supplemental Indenture (among other things) AirTran LLC, as successor by merger to AirTran Holdings Inc, assumed the obligations of AirTran Holdings Inc, as the original “Company” under the Indenture, under the Indenture and Securities;

WHEREAS, Southwest, Pedernales Debt Sub LLC, a Texas limited liability company (“TX Debt Sub”), and the Trustee were the original parties to a Fourth Supplemental Indenture dated as of May 3, 2011, which supplements the Base Indenture, the First Supplemental Indenture, the Second Supplemental Indenture and the Third Supplemental Indenture (the “Fourth Supplemental Indenture” and, the Base Indenture as supplemented by the First Supplemental Indenture, the Second Supplemental Indenture, the Third Supplemental Indenture and the Fourth Supplemental Indenture, the “Indenture”), pursuant to which Fourth Supplemental Indenture (among other things) TX Debt Sub, as successor by merger to AirTran LLC, assumed the obligations of AirTran LLC, as the Company, under the Indenture and Securities;

WHEREAS, Southwest and TX Debt Sub entered into the Agreement and Plan of Merger dated as of May 3, 2011 (the “Merger Agreement”), pursuant to which, at the effective time of the Merger contemplated thereby, TX Debt Sub was merged with and into Southwest such that the separate limited liability company existence of TX Debt Sub ceased and Southwest continued as the surviving corporation;

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WHEREAS, pursuant to Section 6.01 of the First Supplemental Indenture, TX Debt Sub, as the Company under the Indenture, shall not merge into any other Person unless the surviving Person is a corporation or limited liability company organized and validly existing under the laws of the United States or any state thereof, and such Person expressly assumes, by an indenture supplemental to the Indenture, executed and delivered to the Trustee, in form reasonably satisfactory to the Trustee, all of the obligations of the Company under the Securities and the Indenture;

WHEREAS, in accordance with Section 8.01 of the First Supplemental Indenture, Southwest and the Trustee may amend or supplement the Indenture as provided in this Supplemental Indenture without notice to, or consent of, any Securityholder;

WHEREAS, Southwest has duly authorized the execution and delivery of this Supplemental Indenture;

WHEREAS, the Southwest has furnished the Trustee with an Opinion of Counsel and an Officer’s Certificate in accordance with the Indenture, stating that the execution of this Supplemental Indenture is authorized or permitted by the Indenture; and

WHEREAS, all things necessary to make this Supplemental Indenture a valid agreement of Southwest and the Trustee and a valid amendment of, and supplement to, the Indenture have been done, and the entry into this Supplemental Indenture by the parties hereto is in all respects authorized by the provisions of the Indenture.

NOW, THEREFORE, in consideration of the premises set forth herein and for other good and valuable consideration, the receipt of which is hereby acknowledged, the parties hereto covenant and agree for the equal and proportionate benefit of all Holders of the Securities, as follows:

ARTICLE I

CONFIRMATION OF INDENTURE; ASSUMPTION

Section 1.01 Confirmation of Indenture. Except as supplemented hereby, the Indenture is hereby ratified, confirmed, and reaffirmed in all respects. The Indenture and this Supplemental Indenture shall be read, taken, and construed as one and the same instrument.

Section 1.02 Assumption. Pursuant to, and in compliance and in accordance with, Section 6.01 of the First Supplemental Indenture, the Successor Company hereby expressly and unconditionally assumes all of the obligations of the Company under the Securities and the Indenture, including, without limitation, the due and punctual payment of the principal of, premium, if any, and interest on, the Securities and the due and punctual observance of each and every covenant and condition of the Company under the Indenture, all as if the Successor Company were originally the Company thereunder.

Section 1.03 Successor Substituted. In accordance with Section 6.02 of the First Supplemental Indenture, upon the merger of TX Debt Sub into the Successor Company, the Successor Company succeeded to, and was substituted for, and may exercise every right and power of, TX Debt Sub as the “Company” under the Indenture with the same effect as if the Successor Company had been named as the Company in the Indenture.

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Section 1.04 Representations and Warranties. The Successor Company represents that (a) it has all necessary power and authority to execute and deliver this Supplemental Indenture and to perform the Indenture, (b) it is the successor by merger to TX Debt Sub pursuant to a valid merger effected in accordance with applicable law, (c) it is a corporation organized and validly existing under the laws of the State of Texas, (d) both before and immediately after giving effect to this Supplemental Indenture, no Default or Event of Default has or will have occurred or be continuing, and (e) this Supplemental Indenture is executed and delivered pursuant to Section 8.01 of the First Supplemental Indenture and does not require the consent of Securityholders.

ARTICLE II

Definitions

Section 2.01 Definitions. Section 1.02 of the First Supplemental Indenture is hereby amended as follows:

(a) The definition of “Company” and “Southwest” are hereby amended and restated in their entirety to read as one definition as follows:

“Company” and “Southwest” each mean Southwest Airlines Co., a Texas corporation, until a successor replaces it pursuant to the applicable provisions of the First Supplemental Indenture, and thereafter “Company” and “Southwest” shall mean such successor Company. For all purposes of the Indenture, the Company means Southwest and Southwest means the Company, mutatis mutandis. Any reference to both Southwest and the Company shall hereafter mean only Southwest.

ARTICLE III

MISCELLANEOUS PROVISIONS

Section 3.01 Concerning the Trustee. The Trustee assumes no duties, responsibilities, or liabilities by reason of this Supplemental Indenture other than as set forth in the Indenture. The Trustee shall not be responsible in any manner whatsoever for or in respect of the validity or sufficiency of this Supplemental Indenture or for or in respect of the recitals contained herein, all of which recitals are made solely by Southwest. In addition, and without limiting the foregoing, the Trustee is not charged with knowledge of the Merger Agreement or any of the terms thereof.

Section 3.02 Supplemental Indenture Controls. In the event of a conflict or inconsistency between the Indenture and this Supplemental Indenture, the provisions of this Supplemental Indenture shall control.

Section 3.03 Governing Law. THIS SUPPLEMENTAL INDENTURE AND THE SECURITIES SHALL BE GOVERNED BY, AND CONSTRUED IN ACCORDANCE WITH, THE LAWS OF THE STATE OF NEW YORK.

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Section 3.04 No Adverse Interpretation of Other Agreements. This Supplemental Indenture may not be used to interpret another indenture, loan, or debt agreement other than the Indenture for purposes of the Securities. Any such indenture, loan, or debt agreement may not be used to interpret this Supplemental Indenture.

Section 3.05 Multiple Counterparts. The parties may sign multiple counterparts of this Supplemental Indenture. Each signed counterpart shall be deemed an original, but all of them together shall represent the same agreement.

Section 3.06 Headings. The titles and headings of the articles and sections of this Supplemental Indenture have been inserted for convenience of reference only, are not to be considered a part hereof, and shall in no way modify or restrict any of the terms or provisions hereof.

Section 3.07 Successors and Assigns. All covenants and agreements made by Southwest in this Supplemental Indenture shall be binding upon their respective successors and assigns, whether expressed or not.

[Signature Page Follows]

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IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed.

Signature Page to 5.25% Fifth Supplemental Indenture

IN WITNESS WHEREOF, the parties hereto have caused this Supplemental Indenture to be duly executed.

Signature Page to 5.25% Fifth Supplemental Indenture