FILED PURSUANT TO RULE 424(B)(3)
                                                     REGISTRATION NO. 333-105006


PROSPECTUS SUPPLEMENT
(TO PROSPECTUS DATED MAY 5, 2004)


                                 $1,750,000,000

                            LIBERTY MEDIA CORPORATION

                  .75% EXCHANGEABLE SENIOR DEBENTURES DUE 2023


                               -------------------


             (Exchangeable for Time Warner Inc. Common Stock or the
 value thereof in cash and/or Liberty Media Corporation Series A Common Stock)

     This prospectus supplement supplements the prospectus dated May 5, 2004 of
Liberty Media Corporation, relating to $1,750,000,000 aggregate original
principal amount of our .75% exchangeable senior debentures due 2023, which may
be sold from time by the selling security holders named therein and in any
prospectus supplement. You should read this prospectus supplement in conjunction
with the prospectus, and this prospectus supplement is qualified by reference to
the prospectus, except to the extent that the information in this prospectus
supplement supersedes the information contained in the prospectus.


                               -------------------


     INVESTING IN THE DEBENTURES INVOLVES RISKS. YOU SHOULD CAREFULLY CONSIDER
THE MATTERS DESCRIBED UNDER THE CAPTION "RISK FACTORS" BEGINNING ON PAGE 7 OF
THE PROSPECTUS.

     NEITHER THE SECURITIES AND EXCHANGE COMMISSION NOR ANY STATE SECURITIES
COMMISSION HAS APPROVED OR DISAPPROVED OF THESE SECURITIES OR DETERMINED IF THE
PROSPECTUS OR THIS PROSPECTUS SUPPLEMENT IS TRUTHFUL OR COMPLETE. ANY
REPRESENTATION TO THE CONTRARY IS A CRIMINAL OFFENSE.












           The date of this Prospectus Supplement is February 14, 2005


                                      S-1

      Saranac Capital Management L.P. (i) informed us that the group that had
provided investment management services through Salomon Brothers Asset
Management, Inc., a part of Citigroup, Inc., formed Saranac Capital Management
L.P., an entity independent of Citigroup, Inc., and that as of November 1, 2004,
Saranac Capital Management L.P. was appointed as the sub-advisor to the hedge
funds that the group had previously managed through Salomon Brothers Asset
Management, Inc., and (ii) requested that all of the debentures held on behalf
of its clients under the name of Salomon Brothers Asset Management, Inc. reflect
its name change to Saranac Capital Management L.P.

      S.A.C. Arbitrage Fund, LLC informed us that the debentures held by S.A.C.
Capital Associates, LLC and listed in the prospectus under the name of S.A.C.
Capital Associates, LLC were transferred to S.A.C. Capital Associates, LLC's
wholly owned subsidiary, S.A.C. Arbitrage Fund, LLC, in a transaction exempt
from the registration requirements of the Securities Act of 1933, as amended.
S.A.C. Arbitrage Fund, LLC has requested that the debentures be listed under the
name of S.A.C. Arbitrage Fund, LLC.

     The table below sets forth for (i) Salomon Brothers Asset Management, Inc.
and S.A.C. Capital Associates, LLC, who were listed in the prospectus as
"selling security holders," as that term is used in the prospectus and in any
prospectus supplement, of the debentures, the amount of debentures they were
entitled to sell pursuant to the prospectus prior to the filing of this
prospectus supplement, and (ii) Saranac Capital Management L.P. and S.A.C.
Arbitrage Fund, LLC, the amount of debentures that may be sold by such selling
security holders pursuant to the prospectus, as supplemented hereby.



                                                                            PRINCIPAL
                                                                            AMOUNT OF            PERCENTAGE OF
                                                                            DEBENTURES            OUTSTANDING
NAME                                                                    THAT MAY BE SOLD($)       DEBENTURES
----                                                                    -------------------       ----------
                                                                                           
Saranac Capital Management L.P.                                             45,526,000               2.6%

NAME AND AMOUNT OF DEBENTURES LISTED IN THE PROSPECTUS
------------------------------------------------------
Salomon Brothers Asset Management, Inc.                                     62,000,000               3.5%


NAME
----
S.A.C. Arbitrage Fund, LLC                                                   2,000,000                 *

NAME AND AMOUNT OF DEBENTURES LISTED IN THE PROSPECTUS
------------------------------------------------------
S.A.C. Capital Associates, LLC                                               2,000,000                 *



----------
* Less than 1%.

      We prepared the above table based on information supplied to us by the
selling security holders named in the table. Salomon Brothers Asset Management,
Inc. informed us in connection with its request to be named as a selling
security holder in the prospectus that:

      -  it is an affiliate of a registered broker-dealer;

      -  it acquired its debentures in the ordinary course of business; and

      -  at the time of the purchase of its debentures, it had no agreements or
         understandings, directly or indirectly, with any person to distribute
         the debentures.

Except as set forth above with respect to Salomon Brothers Asset Management,
Inc., each of the selling security holders also informed us that:

      -  it is not a registered broker-dealer or an affiliate of a registered
         broker-dealer; and

      -  it has not had any material relationship with us or our affiliates
         during the past three years.


                                      S-2