Form of Global Note representing all 2.750% Notes Due 2022

Exhibit 4.1

THIS SECURITY IS A GLOBAL SECURITY WITHIN THE MEANING OF THE INDENTURE HEREINAFTER REFERRED TO AND IS REGISTERED IN THE NAME OF A DEPOSITARY OR A NOMINEE OF A DEPOSITARY. THIS SECURITY IS EXCHANGEABLE FOR SECURITIES REGISTERED IN THE NAME OF A PERSON OTHER THAN THE DEPOSITARY OR ITS NOMINEE ONLY IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE INDENTURE, AND, EXCEPT IN SUCH LIMITED CIRCUMSTANCES, MAY NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITARY TO A 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 OF THE DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR.

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 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 HEREIN.

SOUTHWEST AIRLINES CO.

2.750% Notes Due 2022

Southwest Airlines Co., a corporation duly organized and existing under the laws of Texas (herein called the “Company,” which term includes any successor corporation under the Indenture hereinafter referred to), for value received, hereby promises to pay to Cede & Co., or registered assigns, the principal sum of THREE HUNDRED MILLION DOLLARS on November 16, 2022, and to pay interest thereon from November 16, 2017 or from the most recent Interest Payment Date (as hereinafter defined) to which interest has been paid or duly provided for, semi-annually in arrears on May 16 and November 16 (each, an “Interest Payment Date”) in each year, commencing May 16, 2018, at the rate of 2.750% per annum, until the principal hereof is fully paid or made available for full payment. Interest on this Security shall be computed on the basis of a 360-day year of twelve 30-day months. The interest so payable, and punctually paid or duly provided for, on any Interest Payment Date will, subject to certain exceptions provided in such Indenture, be paid to the person in whose name this Security is registered on the Security register or registers of the Company at the close of business on May 1 or November 1 (whether or not a Business Day), as the case may be, next preceding such Interest Payment Date.

Payment of the principal of and interest on this Security will be made in such immediately available funds of the United States of America as at the time of payment are legal tender for payment of public and private debts.

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

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

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

Dated: November 16, 2017

ATTEST:

TRUSTEE’S CERTIFICATE OF AUTHENTICATION

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

WELLS FARGO BANK, NATIONAL ASSOCIATION

as Trustee

This Security is one of a duly authorized issue of debt securities of the Company, issued and to be issued in one or more series under an Indenture, dated as of September 17, 2004 (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 Indenture, all indentures supplemental thereto, and the Officers’ Certificate dated November 16, 2017, setting forth the terms of the debt securities of this series, reference is hereby made for a statement of the respective rights, limitation of rights, duties, and immunities thereunder of the Company, the Trustee, and the holders of the Securities (as defined below) and of the terms upon which the Securities are, and are to be, authenticated and delivered. This Security is one of a series designated as 2.750% Notes Due 2022 (the “Securities”). This Security is a Global Security representing the entire principal amount of Securities, initially limited in aggregate principal amount to $300,000,000, but subject to the right of the Company to issue and sell additional Securities in the future without the consent of the holders thereof. Any additional securities of this series, together with this Security, shall constitute a single series under the Indenture.

Redemption

The Securities shall be redeemable, at the option of the Company, in whole or in part, at any time, on at least 20 days but not more than 60 days’ prior notice sent to the registered address of each holder of Securities to be so redeemed. If the Securities are redeemed at any time prior to the Par Call Date, the Securities will be redeemed at a redemption price equal to the greater of (i) 100% of the principal amount of the Securities to be so redeemed and (ii) the sum of the present values of the remaining scheduled payments of principal and interest on such Securities that would have been made if the Securities matured on the Par Call Date (exclusive of interest accrued to the redemption date) discounted to the redemption date, on a semi-annual basis (assuming a 360-day year consisting of twelve 30-day months), at the Treasury Rate (as defined herein) plus 15 basis points, plus, in either case, accrued and unpaid interest on the principal amount being redeemed to such redemption date. If the Securities are redeemed on or after the Par Call Date, the Securities will be redeemed at a redemption price equal to 100% of the principal amount of the Securities to be redeemed, plus accrued and unpaid interest thereon to the redemption date. In either case, the redemption is subject to the right of holders of record on the relevant record date to receive interest due on an Interest Payment Date that is on or before the date of redemption.

If fewer than all of the Securities are to be redeemed at any time, selection of Securities for redemption will be made by the Trustee in such manner as the trustee deems appropriate and fair (or, in the case of Securities issued in global form, by such other method as the DTC may require); provided, however, that the Securities will be redeemed only in the minimum denominations of $2,000 and integral multiples thereof of $1,000.

For purposes of determining the redemption price, the following definitions shall apply:

“Comparable Treasury Issue” means the United States Treasury security selected by the Quotation Agent as having an actual or interpolated maturity comparable to the remaining term of the Securities to be redeemed, calculated as if the maturity date of the Securities were the Par Call Date (the “Remaining Life”), 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 Life.

“Comparable Treasury Price” means, with respect to any redemption date, the average of the Reference Treasury Dealer Quotations for such redemption date.

“Par Call Date” means October 16, 2022 (one month prior to the maturity date).

“Quotation Agent” means one of the Reference Treasury Dealers appointed by the Company.

“Reference Treasury Dealer” means each of Citigroup Global Markets Inc., Goldman Sachs & Co. LLC, and Morgan Stanley & Co. LLC and their respective successors; provided, however, that if any of the foregoing shall cease to be a primary U.S. Government securities dealer in New York City (a “Primary Treasury Dealer”), the Company will substitute therefor another Primary Treasury Dealer.

“Reference Treasury Dealer Quotations” means, with respect to each Reference Treasury Dealer and any redemption date, the average, as determined by the Company, 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 Company and the Trustee by such Reference Treasury Dealer at 3:30 p.m., New York City time, on the third Business Day preceding such redemption date.

“Treasury Rate” means, with respect to any redemption date, the rate per year equal to the semi-annual equivalent yield to maturity or interpolated yield (on a day count basis) 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 redemption date. The Treasury Rate shall be calculated by the Quotation Agent on the third Business Day preceding such redemption date.

Any such redemption may, at the Company’s discretion, be conditioned upon (i) the occurrence of a Change of Control (as defined below) or (ii) the closing of another transaction, including a sale of securities or other financing, in each case as specified in the notice in reasonable detail. A notice of conditional redemption will be of no effect unless all conditions to the redemption have occurred on or before the redemption date or have been waived by the Company on or before the redemption date. The Company will provide notice of the satisfaction of all conditions as soon as practicable following occurrence of the conditions. The Company will provide notice of any waiver of a condition or failure to meet such conditions no later than the redemption date.

Change of Control

Upon the occurrence of a Change of Control Triggering Event, unless the Company has otherwise exercised its right to redeem the Securities, each holder of such Securities will have the right to require the Company to purchase all or a portion of such holder’s Securities pursuant to the offer described below (the “Change of Control Offer”), at a purchase price equal to 101% of the principal amount thereof, plus accrued and unpaid interest thereon, if any, to the date of purchase, subject to the rights of holders of Securities on the relevant record date to receive interest due on the relevant Interest Payment Date.

Within 30 days following the date upon which the Change of Control Triggering Event occurred, or at the Company’s option, prior to any Change of Control but after the public announcement of the Change of Control, unless the Company has otherwise exercised the Company’s right to redeem the Securities, the Company shall deliver a notice to each holder of Securities, with a copy to the Trustee, which notice will govern the terms of the Change of Control Offer. Such notice will state, among other things, the purchase date, which must be no earlier than 30 days nor later than 60 days from the date such notice is sent, other than as may be required by law (the “Change of Control Payment Date”). The notice, if sent prior to the date of consummation of the Change of Control, will state that the Change of Control Offer is conditioned on the Change of Control Triggering Event occurring on or prior to the Change of Control Payment Date. Holders of Securities electing to have Securities purchased pursuant to a Change of Control Offer must surrender their Securities, with the form entitled “Option of Holder to Elect Purchase” on the reverse of the Security completed, to the Paying Agent at the address specified in the notice, or transfer their Securities to the Paying Agent by book-entry transfer pursuant to the applicable procedures of DTC, before the close of business on the third Business Day prior to the Change of Control Payment Date.

The Company will not be required to make a Change of Control Offer if a third party makes such an offer in the manner, at the times and otherwise in compliance with the requirements for such an offer made by the Company and such third party purchases all Securities properly tendered and not withdrawn under its offer.

If holders of not less than 90% in aggregate principal amount of the outstanding Securities validly tender and do not withdraw the Securities in a Change of Control Offer and the Company, or any third party making a Change of Control Offer in lieu of the Company, purchases all of the Securities validly tendered and not withdrawn by such holders, the Company will have the right, upon not less than 20 nor more than 60 days’ prior notice, given not more than 30 days following such purchase pursuant to the Change of Control Offer described above, to redeem all Securities that remain outstanding following such purchase at a redemption price in cash equal to 101% of the principal amount thereof, plus accrued and unpaid interest thereon, if any, to the date of redemption (subject to the right of holders of record on the relevant record date to receive interest on the relevant Interest Payment Date).

The Company will comply with the requirements of Rule 14e-1 under the Securities Exchange Act of 1934 (the “Exchange Act”) and any other securities laws and regulations thereunder to the extent those laws and regulations are applicable in connection with the repurchase of the Securities as a result of a Change of Control Triggering Event. To the extent that the provisions of any such securities laws or regulations conflict with the change of control offer provisions of the Securities, the Company will comply with those securities laws and regulations and will not be deemed to have breached its obligations under the change of control offer provisions of the Securities by virtue of any such conflict.

Except as described above with respect to a Change of Control Triggering Event, the holders of the Securities shall not have any right to require the Company to repurchase or redeem the Securities in the event of a takeover, recapitalization, or similar transaction.

As used herein:

“Below Investment Grade Rating Event” means the rating on the Securities is lowered by each of the Rating Agencies and the Securities are rated below Investment Grade by each of the Rating Agencies on any day within the 60-day period (which 60-day period will be extended so long as the rating of the Securities is under publicly announced consideration for a possible downgrade by any of the Rating Agencies) after the earlier of (1) the occurrence of a Change of Control or (2) public notice of the occurrence of a Change of Control or the Company’s intention to effect a Change of Control; provided that a Below Investment Grade Rating Event otherwise arising by virtue of a particular reduction in rating shall not be deemed to have occurred in respect of a particular Change of Control (and thus shall not be deemed a Below Investment Grade Rating Event for purposes of the definition of Change of Control Triggering Event) if the Rating Agencies making the reduction in rating to which this definition would otherwise apply do not announce or publicly confirm or inform the Company and the Trustee in writing at its request that the reduction was the result, in whole or in part, of any event or circumstance comprised of or arising as a result of, or in respect of, the applicable Change of Control (whether or not the applicable Change of Control shall have occurred at the time of the Below Investment Grade Rating Event).

“Change of Control” means the consummation of any transaction (including without limitation, any merger or consolidation) the result of which is that any “person” (as that term is used in Section 13(d)(3) of the Exchange Act), other than the Company or its subsidiaries, becomes the beneficial owner (as defined in Rules 13d-3 and 13d-5 under the Exchange Act), directly or indirectly, of more than 50% of the combined voting power of the Company’s Voting Stock or other Voting Stock into which the Company’s Voting Stock is reclassified, consolidated, exchanged, or changed measured by voting power rather than number of shares, other than any such transaction where:

(a) the Company’s outstanding Voting Stock is reclassified, consolidated, exchanged, or changed for other Voting Stock of the Company or for Voting Stock of the surviving corporation, and

(b) the holders of the Company’s Voting Stock immediately before that transaction own, directly or indirectly, not less than a majority of the Company’s Voting Stock or the Voting Stock of the surviving parent corporation immediately after such transaction and in substantially the same proportion as their ownership in the Company before the transaction.

“Change of Control Triggering Event” means the occurrence of both a Change of Control and a Below Investment Grade Rating Event.

“Fitch” means Fitch Ratings, Inc. and its successors.

“Investment Grade” means a rating of BBB- or better by Fitch (or its equivalent under any successor rating category of Fitch); a rating of Baa3 or better by Moody’s (or its equivalent under any successor rating category of Moody’s); and a rating of BBB- or better by S&P (or its equivalent under any successor rating category of S&P).

“Moody’s” means Moody’s Investors Service, Inc., a subsidiary of Moody’s Corporation, and its successors.

“Rating Agency” means (1) each of Fitch, Moody’s, and S&P, and (2) if any of Fitch, Moody’s, or S&P ceases to rate the Securities or fails to make a rating of the Securities publicly available for reasons outside of the Company’s control, a “nationally recognized statistical rating organization” as defined in Section 3(a)(62) of the Exchange Act, selected by the Company (as certified by a resolution of the Company’s board of directors) as a replacement agency for Fitch, Moody’s, or S&P, or all of them, as the case may be.

“S&P” means S&P Global Ratings, a division of S&P Global Inc., and its successors.

“Voting Stock” of any specified person as of any date means the capital stock of such person that is at the time entitled to vote generally in the election of the board of directors of such person.

Supplemental Indentures

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 at the time outstanding of all series to be affected (voting as one class), evidenced as in the Indenture provided, to execute supplemental indentures adding any provisions to or changing in any manner or eliminating any of the provisions of the Indenture or of any supplemental indenture or modifying in any manner the rights of the holders of the Securities of each such series; provided, however, that no such supplemental indenture shall (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 any interest thereon, or reduce any amount payable on redemption thereof or impair or affect the right of any holder of Securities to institute suit for payment thereof or right of repayment, if any, at the option of a holder of the Securities, without the consent of the holder of each Security so affected, or (ii) reduce the percentage of aggregate principal amount of Securities of any series or of all series (voting as one class), as the case may be, the holders of which are required to consent to any such supplemental indenture, without the consent of the holders of all outstanding Securities of each such series so affected.

Denominations

The Securities are in registered form without coupons in minimum denominations of $2,000 and integral multiples of $1,000 in excess thereof.

Exchange

This Global Security shall be exchangeable for Securities registered in the names of persons other than the Depositary for such Global Security or its nominee only as provided in this paragraph. This Global Security shall be so exchangeable if (x) the Depositary notifies the Company that it is unwilling or unable to continue as Depositary for this Global Security or if at

any time such Depositary ceases to be a clearing agency registered as such under the Exchange Act, and the Company fails to appoint a successor Depositary for this Global Security within 90 days after the Company receives such notice or becomes aware of such event, (y) the Company executes and delivers to the Trustee written instructions that this Global Security shall be so exchangeable, or (z) there shall have occurred and be continuing an Event of Default or an event which, with the giving of notice or lapse of time, or both, would constitute an Event of Default with respect to the Securities. Securities so issued in exchange for this Global Security shall be of the same series and of like tenor, in authorized denominations and in the aggregate having the same principal amount as this Global Security and registered in such names as the Depositary for such Global Security shall direct.

Transfer

As provided in the Indenture and subject to certain limitations therein set forth, the transfer of this Security is registrable in the Security register or registers of the Company, 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 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 registered holder hereof or its attorney duly authorized in writing, and thereupon on or more new Securities, and of like tenor, of authorized denominations and for the same aggregate principal amount, will be issued to the designated transferee or transferees. At the date of the Indenture, such agency of the Company is located at the office of Wells Fargo Bank, National Association, at 1445 Ross Avenue, Suite 4300, Dallas, Texas 75202.

No service charge shall be made for any such exchange or registration of transfer, but the Company or the Securities registrar 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 payments made to or upon the order of such registered holder shall, to the extent of the sum or sums paid, effectually satisfy and discharge liability for moneys payable on this Security.

Miscellaneous

The Securities are not subject to any sinking fund.

The Indenture contains provisions for defeasance of the entire indebtedness of the Securities upon compliance by the Company with certain conditions set forth therein.

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

All terms used in this Security that are defined in the Indenture shall have the meanings assigned to them in the Indenture.

The Indenture and the Securities shall be governed by and construed in accordance with the laws of the State of Texas.

Option of Holder to Elect Purchase

If you want to elect to have this Security purchased by the Company pursuant to the Change of Control Offer of the Indenture, check the box below:

If you want to elect to have only part of the Security purchased by the Company pursuant to Change of Control Offer of the Indenture, state the amount you elect to have purchased (in minimum denominations of $2,000 and integral multiples thereof of $1,000, except if you have elected to have all of your Securities purchased): $

Signature Guarantee*