Exhibit 10.4

Pursuant to the terms of the Southwest Airlines Co. Amended and Restated 2007 Equity Incentive Plan (the “Plan”), Southwest Airlines Co. (the “Company”) hereby grants to you (the “Participant”) an award of performance-based restricted stock units (“PBRSUs”) as follows:

The number of PBRSUs that will vest and the number of shares of the Company’s common stock to be issued, if any, as of the Vesting Date will be determined based upon the achievement of the targets set forth in the schedule below. The percentage of PBRSUs vesting will be interpolated between the targets set forth in the schedule below. On the Vesting Date, it will be a condition to vesting that the Participant has continuously served as an Employee, Director, or Advisor (each as defined in the Plan) from the Date of Grant through the Vesting Date; provided that special terms will apply if termination of service is due to death or disability (see enclosed Terms and Conditions).

Participant understands and agrees that the PBRSUs are granted in accordance with, and subject to, the terms and conditions of the Plan and the Terms and Conditions enclosed with this Notice of Grant. The Plan and the prospectus for the Plan are enclosed with this Notice of Grant. Additional copies of these documents are available upon request to the Company’s Stock Plan Administration Department.

By asserting any rights with respect to performance-based Restricted Stock Units (“PBRSUs” or “Performance-Based Restricted Stock Units”) received pursuant to the Southwest Airlines Co. Amended and Restated 2007 Equity Incentive Plan (the “Plan”), the recipient of the PBRSUs (the “Participant”) will be deemed to have understood and agreed to the terms and conditions of the Plan and the terms and conditions set forth below. Capitalized terms used and not otherwise defined herein shall have the meanings assigned to them in the Plan.

1.    Vesting. Subject to these Terms and Conditions and the provisions of the Plan, vesting of the PBRSUs will be subject to and in accordance with the schedule set forth in the Notice of Grant with which these Terms and Conditions are enclosed.

2.    Interpretation. The Participant’s Performance-Based Restricted Stock Unit Award is subject to the terms and conditions of the Plan, which terms and conditions are incorporated herein by reference. The Participant’s Performance-Based Restricted Stock Unit Award is also subject to any rules promulgated pursuant to the Plan by the Board, the Committee, or the persons designated by the Committee to administer the day-to-day administration of the Plan. Any decisions or interpretations upon any questions with respect to a Performance-Based Restricted Stock Unit Award or the Plan, including the determination of the number of shares of Common Stock to be received upon settlement of the Participant’s Performance-Based Restricted Stock Units, shall (as permissible pursuant to applicable laws, rules, or regulations, including the rules of any stock exchange upon which the Company’s Common Stock is listed or quoted) be determined (i) by the Committee, (ii) by the Board, or (iii) where permitted by the Committee, by any person(s) to whom the Committee has delegated its authority. The Participant (and any person who has acquired the PBRSUs by will or the laws of descent and distribution or intestacy) agrees to accept any such decisions or interpretations as binding, conclusive, and final in all respects.

3.    Settlement of Performance-Based Restricted Stock Units. Subject to these Terms and Conditions and the provisions of the Plan, upon the vesting date, the Participant (or any person who has acquired the PBRSUs by will or the laws of descent and distribution or intestacy) will become entitled to delivery of one share of Common Stock for each Performance-Based Restricted Stock Unit that vests, as determined in accordance with the schedule set forth in the Notice of Grant (the “Vested Shares”). As soon as is administratively and reasonably practicable thereafter (but in any event, no later than 30 days thereafter), such Vested Shares will be registered in the Participant’s name or otherwise delivered or credited for the Participant’s account or benefit (in each case as determined by the Company), subject to (a) the Participant’s satisfaction of any Tax Obligations (as defined in Section 5 below); (b) the Participant’s taking of any additional action deemed necessary or advisable by the Company to enable it to accomplish the delivery of the shares of Common Stock; and (c) the condition precedent that, if at any time the Board or the Committee shall determine in their discretion that the listing, registration, or qualification of the Vested Shares is required under any federal, state, or other law, rule, or regulation, or by the requirements of any securities exchange, or that the consent or approval of any governmental regulatory body is necessary or desirable as a condition of, or in connection with, the issuance of the Vested Shares, then the PBRSUs will not vest in whole or in part unless and until such listing, registration, qualification, consent, or approval shall have been effected or obtained free of any conditions not acceptable to the Board or the Committee; provided, however, in the event any action required by clause (a) or (b) above has not been completed by the Participant on or before

March 10 of the calendar year immediately following the calendar year in which Performance-Based Restricted Stock Units have become Vested Shares, such Performance-Based Restricted Stock Units will be forfeited at 4:00 p.m., Eastern Time, on such date. No fractional shares of Common Stock will be issued in settlement of the PBRSUs.

5.    Taxes.

a.In order to comply with any federal, state, local, or other laws or regulations of the United States or any other applicable jurisdiction, the Company or any Affiliate is authorized to take such action as it shall deem appropriate to provide that all applicable federal, state, local, or other income, employment, or other tax withholding or similar obligations (collectively, “Tax Obligations”) to which the Participant is subject in connection with the PBRSUs are withheld or collected from the Participant. If and to the extent permitted by the Committee from time to time, the Company is authorized to satisfy the Tax Obligations by any one or more of the following methods: (i) by requiring the Participant to pay such amount in cash or check; (ii) by withholding a number of shares of Common Stock that would otherwise be issued with respect to the PBRSUs having a market value sufficient to meet the Tax Obligations; (iii) by instructing the Plan administrator to sell, or cause to be sold, on behalf of the Participant a number of Vested Shares having a market value equal to the amount of the Tax Obligations (plus sales commissions) to which the Participant is subject, and the Participant hereby appoints the Corporate Secretary of the Company as the Participant’s attorney-in-fact, with full power of substitution and resubstitution, to execute such sale; (iv) by deducting the amount of the Tax Obligations out of any other remuneration otherwise payable by the Company to the Participant; or (v) by such other method as may become available to the Company from time to time.

b.The Participant is ultimately liable and responsible for all of the Participant’s Tax Obligations, regardless of any action taken by the Company in accordance with Section 5.a. The Company makes no representation or undertaking regarding the treatment of any Tax Obligation in connection with the grant, vesting, or settlement of the PBRSUs or the subsequent sale of any of the shares of Common Stock received upon settlement of any PBRSUs. The Company does not commit, and is under no obligation, to structure the Plan and its administration to reduce or eliminate a Participant’s tax liability.

c.The Participant agrees to release and indemnify the Company and its Affiliates from any liability or damages arising from or relating to the Participant’s failure to comply with his or her Tax Obligations.

8.    Adjustment of Number of Shares and Related Matters. The number and kind of shares of Common Stock covered by a Participant’s Performance-Based Restricted Stock Unit Award shall be subject to adjustment in accordance with the terms of the Plan relating to recapitalization or reorganization.

9.    Investment Representation. By accepting any shares of Common Stock issued pursuant to the Participant’s Performance-Based Restricted Stock Unit Award, the Participant represents and warrants to the Company that the receipt of such shares shall be for investment and not with a view to distribution; provided that such representation and warranty shall be inoperative if, in the opinion of counsel to the Company, a proposed distribution of such shares is pursuant to an applicable effective registration statement under the Securities Act of 1933, as amended, or is, without such representation and warranty, exempt from registration under such Act.

10.    No Right to Continued Service and other Participant Acknowledgments. Nothing herein shall be construed to confer upon the Participant any right to continue as an Employee, Director, or Advisor or to interfere with or restrict in any way the right of the Company or any Affiliate to discharge the Participant at any time (subject to any contractual rights of the Participant) for any reason whatsoever, with or without cause and with or without advance notice. Furthermore, nothing herein shall in any way be construed as imposing on the Company or any Affiliate a contractual obligation between the Company or any Affiliate and the Participant, other than with respect to the specific terms of the Participant’s Performance-Based Restricted Stock Unit Award.

11.    Law Governing. The Participant’s Performance-Based Restricted Stock Unit Award shall be governed by, and construed in accordance with, the laws of the State of Texas, without regard to conflicts of laws principles thereof.

12.    Legal Construction. In the event that any one or more of these Terms and Conditions shall be held by a Court of competent jurisdiction to be invalid, illegal, or unenforceable in any respect for any reason, the invalid, illegal, or unenforceable term or condition shall not affect any other term or condition, and these Terms and Conditions shall be construed in all respects as if the invalid, illegal, or unenforceable term or condition had never been contained herein.

13.    Amendments. The Plan and the PBRSUs may be amended or altered by the Board or the Committee to the extent provided in the Plan.