<PAGE>
 
                                                                     EXHIBIT 4.1



          This FIRST SUPPLEMENTAL INDENTURE (the "First Supplemental Indenture")
          among FOX/LIBERTY NETWORKS, LLC ("Networks"), a Delaware limited
          liability company, FLN FINANCE, INC. ("FLN"), a Delaware corporation,
          and THE BANK OF NEW YORK, a New York banking corporation (the
          "Trustee"), as trustee, is made and entered into as of March 31, 1998.

                              W I T N E S S E T H
                              - - - - - - - - - -

     WHEREAS, Networks and FLN have executed and delivered to the Trustee an
Indenture dated as of August 25, 1997 (the "Original Indenture" and, as
supplemented by this First Supplemental Indenture, the "Indenture"), providing
for the issuance and sale by Networks and FLN of Series A Senior Notes Due 2007
(the "Initial Notes") and Series B Senior Notes Due 2007 issued pursuant to an
exchange for Initial Notes; and

     WHEREAS, all capitalized items used herein which are defined in the
Original Indenture shall have the meanings assigned to them in the Original
Indenture unless otherwise defined herein; and

     WHEREAS, Section 9.1 of the Original Indenture permits amendments to the
Original Indenture without the consent of the Holders under certain conditions;
and

     WHEREAS, Networks and FLN, pursuant to the foregoing authority, propose in
and by this First Supplemental Indenture, to supplement and amend the Original
Indenture as set forth herein; and

     WHEREAS, Networks and FLN have duly authorized the execution and delivery
of this First Supplemental Indenture;

                           AGREEMENT OF THE PARTIES

     NOW, THEREFORE, Networks, FLN and the Trustee, acting pursuant to Section
9.1 of the Original Indenture, hereby agree that the following Articles amend
and supplement the Original Indenture as set forth herein:
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                                   ARTICLE I
                                   ---------

     The following definition contained in Section 1.1 of the Original Indenture
is hereby amended to read in its entirety as follows:

               "Unrestricted Subsidiary" means, as of the date of the Indenture,
          Liberty/Fox Arizona LLC, Prime Ticket Networks, L.P., Liberty/Fox
          Distribution L.P., Liberty/Fox Network Programming, LLC, Rocky
          Mountain Prime Sports Network, SportsChannel Chicago Associates,
          SportsChannel Pacific Associates, Fox Sports Detroit, LLC, Sunshine
          Network, Fox/Liberty Ad Sales, LLC, Liberty/Fox Upper Midwest, LLC,
          Liberty/Fox Canada, LLC and each other Subsidiary of the Company
          designated as such pursuant to and in compliance with Section 10.18.
          Any such Designation may be revoked by Board Resolution of the Company
          delivered to the Trustee, subject to the provisions of Section 10.18.

                                  ARTICLE II
                                  ----------

     The final paragraph of Section 10.18(a) is hereby amended to read in its
entirety as follows:

               The Company shall not, and shall not cause or permit any
          Restricted Subsidiary to, at any time (x) provide credit support for
          or subject any of its property or assets (other than the Capital Stock
          of any Unrestricted Subsidiary) to the satisfaction of, any
          Indebtedness of any Unrestricted Subsidiary (including any
          undertaking, agreement or instrument evidencing such Indebtedness),
          (y) be directly or indirectly liable for any Indebtedness of any
          Unrestricted Subsidiary or (z) be directly or indirectly liable for
          any Indebtedness which provides that the holder thereof may (upon
          notice, lapse of time or both) declare a default thereon or cause the
          payment thereof to be accelerated or payable prior to its final
          scheduled maturity upon the occurrence of a default with respect to
          any Indebtedness of any Unrestricted Subsidiary (including any right
          to take enforcement action against such Unrestricted Subsidiary),
          except as part of or in connection with a Permitted Investment or any
          non-recourse guarantee given solely to support the pledge by the
          Company or any Restricted Subsidiary of the Capital Stock of an
          Unrestricted Subsidiary. No Unrestricted Subsidiary shall at any time
          guarantee or otherwise provide credit support for any obligation of
          the Company or any Restricted Subsidiary, except as provided in the
          Bank Credit Agreement. All Subsidiaries of Unrestricted

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          Subsidiaries shall automatically be deemed to be Unrestricted 
          Subsidiaries.

     Except as specifically modified herein, the Original Indenture is and shall
continue to be in full force and effect and is hereby in all respects ratified
and confirmed.

     This First Supplemental Indenture may be executed in two or more
counterparts, all of which shall be considered the same agreement.

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


                                       FOX/LIBERTY NETWORKS, LLC


                                       By: /s/ Jeff Shell
                                           -------------------------------------
                                       Name:  Jeff Shell
                                       Title: Executive Vice President and Chief
                                              Financial Officer


                                       FLN FINANCE, INC.


                                       By: /s/ Jeff Shell
                                           -------------------------------------
                                       Name:  Jeff Shell
                                       Title: Executive Vice President and Chief
                                              Financial Officer

                                       THE BANK OF NEW YORK


                                       By: /s/ Michael Culhane
                                           -------------------------------------
                                       Name:  Michael Culhane
                                       Title: Vice President

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