<PAGE>   1
                                                                    EXHIBIT 4.10


                           FORM OF RULE 144A SECURITY

THIS SECURITY IS A RULE 144A SECURITY WITHIN THE MEANING OF THE INDENTURE
HEREINAFTER REFERRED TO AND IS REGISTERED IN THE NAME OF A DEPOSITORY (AS
DEFINED IN THE INDENTURE) OR A NOMINEE THEREOF. UNLESS AND UNTIL IT IS EXCHANGED
IN WHOLE OR IN PART FOR SECURITIES IN DEFINITIVE FORM, THIS GLOBAL SECURITY MAY
NOT BE TRANSFERRED EXCEPT AS A WHOLE BY THE DEPOSITORY TO A NOMINEE OF THE
DEPOSITORY, OR BY A NOMINEE OF THE DEPOSITORY TO THE DEPOSITORY OR ANOTHER
NOMINEE OF THE DEPOSITORY, OR BY THE DEPOSITORY OR ANY SUCH NOMINEE TO A
SUCCESSOR DEPOSITORY OR A NOMINEE OF SUCH SUCCESSOR DEPOSITORY.

UNLESS THIS SECURITY IS PRESENTED BY AN AUTHORIZED REPRESENTATIVE OF THE
DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), TO THE COMPANY (AS
DEFINED BELOW) OR ITS AGENT FOR REGISTRATION OF TRANSFER, EXCHANGE OR PAYMENT,
AND ANY SECURITY ISSUED IS REGISTERED IN THE NAME OF CEDE & CO. OR IN SUCH OTHER
NAME AS 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.

THE SECURITY EVIDENCED HEREBY HAS NOT BEEN REGISTERED UNDER THE SECURITIES ACT
OF 1933, AS AMENDED (THE "SECURITIES ACT"), OR ANY STATE OR OTHER SECURITIES
LAWS. NEITHER THIS SECURITY NOR ANY INTEREST OR PARTICIPATION HEREIN MAY BE
REOFFERED, SOLD, ASSIGNED, TRANSFERRED, PLEDGED, ENCUMBERED OR OTHERWISE
DISPOSED OF IN THE ABSENCE OF SUCH REGISTRATION OR UNLESS THE TRANSACTION IS
EXEMPT FROM, OR NOT SUBJECT TO, THE REGISTRATION REQUIREMENTS OF THE SECURITIES
ACT. THE HOLDER OF THIS SECURITY BY ITS ACCEPTANCE HEREOF (1) REPRESENTS THAT
(A) IT IS A "QUALIFIED INSTITUTIONAL BUYER" (AS DEFINED IN RULE 144A UNDER THE
SECURITIES ACT), (B) IT IS AN INSTITUTIONAL "ACCREDITED INVESTOR" WITHIN THE
MEANING OF SUBPARAGRAPH (a)(1), (2), (3) OR (7) OF RULE 501 UNDER THE SECURITIES
ACT) OR (C) IT IS NOT A U.S. PERSON AND IS ACQUIRING THIS SECURITY IN AN
"OFFSHORE TRANSACTION" PURSUANT TO RULE 903 OR 904 OF REGULATION S, (2) AGREES
THAT IT WILL NOT PRIOR TO (X) THE DATE WHICH IS TWO YEARS (OR SUCH SHORTER
PERIOD OF TIME AS PERMITTED BY RULE 144(k) UNDER THE SECURITIES ACT OR ANY
SUCCESSOR PROVISION THEREUNDER) AFTER THE LATER OF THE ORIGINAL ISSUE DATE
HEREOF (OR OF ANY PREDECESSOR OF THIS SECURITY) OR THE LAST DAY ON WHICH THE
COMPANY OR ANY AFFILIATE OF THE COMPANY WAS THE OWNER OF THIS SECURITY (OR ANY
PREDECESSOR OF THIS SECURITY) AND (Y) SUCH LATER DATE, IF ANY, AS MAY BE
REQUIRED BY APPLICABLE LAWS (THE

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"RESALE RESTRICTION TERMINATION DATE"), OFFER, SELL OR OTHERWISE TRANSFER THIS
SECURITY EXCEPT (A) TO THE COMPANY OR ANY SUBSIDIARY THEREOF, (B) PURSUANT TO A
REGISTRATION STATEMENT WHICH HAS BEEN DECLARED EFFECTIVE UNDER THE SECURITIES
ACT, (C) FOR SO LONG AS THE SECURITIES ARE ELIGIBLE FOR RESALE PURSUANT TO RULE
144A, TO A PERSON IT REASONABLY BELIEVES IS A "QUALIFIED INSTITUTIONAL BUYER" AS
DEFINED IN RULE 144A UNDER THE SECURITIES ACT THAT PURCHASES FOR ITS OWN ACCOUNT
OR FOR THE ACCOUNT OF A QUALIFIED INSTITUTIONAL BUYER TO WHOM NOTICE IS GIVEN
THAT THE TRANSFER IS BEING MADE IN RELIANCE ON RULE 144A, (D) INSIDE THE UNITED
STATES TO AN INSTITUTIONAL "ACCREDITED INVESTOR" AS DEFINED IN RULE 501(a)(1),
(2), (3) OR (7) UNDER THE SECURITIES ACT THAT PRIOR TO SUCH TRANSFER, FURNISHES
(OR HAS FURNISHED ON ITS BEHALF BY A U.S. BROKER-DEALER) TO THE TRUSTEE OR
TRANSFER AGENT, A SIGNED LETTER CONTAINING CERTAIN REPRESENTATIONS AND
AGREEMENTS RELATING TO THE RESTRICTIONS ON TRANSFER OF THIS SECURITY (THE FORM
OF WHICH LETTER CAN BE OBTAINED FROM THE TRUSTEE OR TRANSFER AGENT FOR THIS
SECURITY), (E) PURSUANT TO OFFERS AND SALES TO NON-U.S. PERSONS THAT OCCUR
OUTSIDE THE UNITED STATES WITHIN THE MEANING OF REGULATION S UNDER THE
SECURITIES ACT, PURSUANT TO RULE 904 OF REGULATION S OR (F) PURSUANT TO ANOTHER
AVAILABLE EXEMPTION FROM THE REGISTRATION REQUIREMENTS OF THE SECURITIES ACT,
AND (3) AGREES THAT IT WILL GIVE TO EACH PERSON TO WHOM THIS SECURITY IS
TRANSFERRED A NOTICE SUBSTANTIALLY TO THE EFFECT OF THIS LEGEND; PROVIDED THAT
THE COMPANY, THE TRUSTEE AND THE TRANSFER AGENT AND REGISTRAR RESERVE THE RIGHT
PRIOR TO ANY OFFER, SALE OR OTHER TRANSFER PURSUANT TO CLAUSES (D), (E) OR (F)
ABOVE TO REQUIRE DELIVERY OF AN OPINION OF COUNSEL, CERTIFICATIONS AND OTHER
INFORMATION SATISFACTORY TO THE COMPANY, THE TRUSTEE AND THE TRANSFER AGENT AND
REGISTRAR. THIS LEGEND WILL BE REMOVED UPON THE REQUEST OF THE HOLDER AFTER THE
RESALE RESTRICTION TERMINATION DATE. AS USED HEREIN, THE TERMS "OFFSHORE
TRANSACTION," "UNITED STATES" AND "U.S. PERSON" HAVE THE RESPECTIVE MEANINGS
GIVEN TO THEM BY REGULATION S UNDER THE SECURITIES ACT.

THE HOLDER OF THIS SECURITY BY ITS ACCEPTANCE HEREOF AGREES TO BE BOUND BY THE
PROVISIONS OF THE REGISTRATION RIGHTS AGREEMENT RELATING TO ALL THE SECURITIES.


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No. R-1                                                           $1,000,000,000
CUSIP No. 530715AH4

                            LIBERTY MEDIA CORPORATION

                        8-1/4% Senior Debentures due 2030

                               Rule 144A Security

         Liberty Media Corporation, a Delaware corporation (hereinafter called
the "Company", which term includes any successor corporation under the Indenture
referred to below), for value received, hereby promises to pay to Cede & Co., or
registered assigns, the principal sum of One Billion Dollars ($1,000,000,000)
(or such lesser amount as shall be the outstanding principal amount of this U.S.
Global Security shown in Schedule A hereto) on February 1, 2030, and to pay
interest thereon from February 2, 2000 or from the most recent date to which
interest has been paid or provided for, semiannually on February 1 and August 1
in each year (each, an "Interest Payment Date"), commencing August 1, 2000, at
the rate of 8-1/4% per annum, until the principal hereof is paid or made
available for payment. Interest on this Debenture shall be calculated on the
basis of a 360-day year consisting of twelve 30-day months. The interest so
payable and paid or provided for on any Interest Payment Date will, as provided
in such Indenture, be paid to the Person in whose name this Debenture (or one or
more Predecessor Securities) is registered at the close of business on the
Regular Record Date for such interest, which shall be the January 15 or July 15
(whether or not a Business Day), as the case may be, next preceding such
Interest Payment Date. Any such interest which is payable, but is not paid or
provided for, on any Interest Payment Date shall forthwith cease to be payable
to the registered Holder hereof on the relevant Regular Record Date by virtue of
having been such Holder, and may be paid to the Person in whose name this
Debenture (or one or more Predecessor Securities) is registered at the close of
business on a Special Record Date for the payment of such Defaulted Interest to
be fixed by the Company, notice whereof shall be given to the Holders of
Debentures not less than 10 days prior to such Special Record Date, or may be
paid at any time in any other lawful manner not inconsistent with the
requirements of any securities exchange on which the Debentures may be listed,
and upon such notice as may be required by such exchange, all as more fully
provided in such Indenture.

         Payment of the principal of and the interest on this Debenture will be
made at the office or agency of the Company maintained for that purpose in The
Borough of Manhattan, The City of New York, in such coin or currency of the
United States of America as at the time of payment is legal tender for payment
of public and private debts; provided, however, that, at the option of the
Company, interest may be paid by check mailed to the address of the Person
entitled thereto as such address shall appear in the Security Register;
provided, further, that payment to DTC or any successor Depository may be made
by wire transfer to the account designated by DTC or such successor Depository
in writing.

         This Security is a global Rule 144A Security issued on the date hereof
which represents $1,000,000,000 of the principal amount of the Company's 8-1/4%
Senior Debentures due 2030, initially offered and sold to qualified
institutional buyers, as defined in Rule 144A under the Securities Act. This
Debenture is one of a duly authorized issue of securities of the Company



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<PAGE>   4

(herein called the "Debentures") issued and to be issued in one or more series
under an Indenture dated as of July 7, 1999 (herein called, together with the
Third Supplemental Indenture referred to below and all other indentures
supplemental thereto, the "Indenture") between the Company and The Bank of New
York, as Trustee (herein called the "Trustee", which term includes any successor
trustee under the Indenture), to which Indenture and all indentures supplemental
thereto reference is hereby made for a statement of the respective rights,
limitations of rights, duties and immunities thereunder of the Company, the
Trustee and the Holders of the Debentures, and of the terms upon which the
Debentures are, and are to be, authenticated and delivered. This Debenture is
one of the series designated on the face hereof, initially limited (subject to
exceptions provided in the Indenture) to the aggregate principal amount
specified in the Third Supplemental Indenture between the Company and the
Trustee, dated as of February 2, 2000, establishing the terms of the Debentures
pursuant to the Indenture (the "Third Supplemental Indenture").

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

         The Indenture permits, with certain exceptions as therein provided, the
amendment thereof and the modification of the rights and obligations of the
Company and the rights of the Holders of the Securities of each series issued
under the Indenture at any time by 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 each series affected thereby. The
Indenture also contains provisions permitting the Holders of specified
percentages in aggregate principal amount of the Securities of any series at the
time Outstanding, on behalf of the Holders of all Securities of such series, to
waive compliance by the Company with certain provisions of the Indenture and
certain past defaults under the Indenture and their consequences. Any such
consent or waiver by the Holder of this Debenture shall be conclusive and
binding upon such Holder and upon all future Holders of this Debenture and of
any Debentures issued upon the registration of transfer hereof or in exchange
herefor or in lieu hereof, whether or not notation of such consent or waiver is
made upon this Debenture or such Debentures.

         No reference herein to the Indenture and no provision of this Debenture
or of the Indenture shall alter or impair the obligation of the Company, which
is absolute and unconditional, to pay the principal of and interest on this
Debenture, at the times, place and rate, and in the coin or currency, herein and
in the Indenture prescribed.

         As provided in the Indenture and subject to certain limitations set
forth therein and in this Debenture, the transfer of this Debenture may be
registered on the Security Register upon surrender of this Debenture for
registration of transfer at the office or agency of the Company maintained for
the purpose in any place where the principal of and interest on this Debenture
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 Holder hereof or by his attorney duly authorized in writing,
and thereupon one or more new Debentures of this series and of like tenor, of
authorized denominations and for the same aggregate principal amount, will be
issued to the designated transferee or transferees.



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<PAGE>   5

         The Debentures are issuable only in registered form without coupons in
the denominations specified in the Third Supplemental Indenture establishing the
terms of the Debentures, all as more fully provided in the Indenture. As
provided in the Indenture, and subject to certain limitations set forth in the
Indenture and in this Debenture, the Debentures are exchangeable for a like
aggregate principal amount of Debentures of this series in different authorized
denominations, as requested by the Holders surrendering the same.

         No service charge shall be made for any such registration of transfer
or exchange, but the Company may require payment of a sum sufficient to cover
any tax or other governmental charge payable in connection therewith, other than
in certain cases provided in the Indenture.

         Interests in this Debenture are exchangeable or transferable in whole
or in part for interests in the Temporary Regulation S Security or Permanent
Regulation S Security, in each case of the same series, only if such exchange or
transfer complies with the terms for transfer contained in the Indenture.

         Prior to due presentment of this Debenture 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 Debenture is registered as the owner
hereof for all purposes, whether or not this Debenture be overdue, and neither
the Company, the Trustee nor any such agent shall be affected by notice to the
contrary.

         The Indenture contains provisions whereby (i) the Company may be
discharged from its obligations with respect to the Debentures (subject to
certain exceptions) or (ii) the Company may be released from its obligation
under specified covenants and agreements in the Indenture, in each case if the
Company irrevocably deposits with the Trustee money or U.S. Government
Obligations sufficient to pay and discharge the entire indebtedness on all
Debentures of this series, and satisfies certain other conditions, all as more
fully provided in the Indenture.

         This Debenture shall be governed by and construed in accordance with
the laws of the State of New York.

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

         Unless the certificate of authentication hereon has been executed by or
on behalf of the Trustee under the Indenture by the manual signature of one of
its authorized signatories, this Debenture shall not be entitled to any benefits
under the Indenture or be valid or obligatory for any purpose.



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<PAGE>   6

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



                                         LIBERTY MEDIA CORPORATION



Attest:                                  By:
        -----------------------              ----------------------
        Name:                                Name:
        Title:                               Title:


                     TRUSTEE'S CERTIFICATE OF AUTHENTICATION

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

Dated: February 2, 2000                  THE BANK OF NEW YORK,
                                         as Trustee


                                         By:
                                              ----------------------
                                              Authorized Signatory



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<PAGE>   7

                             CERTIFICATE OF TRANSFER


         To transfer or assign this Debenture, fill in the form below:

I or we transfer and assign this Debenture to



--------------------------------------------------------------------------------
                      (Insert assignee's tax I.D. number)

--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
--------------------------------------------------------------------------------
              (Print or Type assignee's name, address and zip code)

and irrevocably appoint ________________ agent to transfer this Debenture on the
books of the Company. The agent may substitute another to act for him.


Date:                             Your signature:
     --------------------------                   --------------------------



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<PAGE>   8

                                   SCHEDULE A

                              SCHEDULE OF EXCHANGES

The following exchanges of Debentures for Debentures represented by this Rule
144A Security have been made:

<TABLE>
<CAPTION>
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Principal amount of                              Change in principal     Principal amount of
this Rule 144A                                   Amount of this Rule     this Rule 144A         Notation made by or
Security as of            Date exchange          144A Security due to    Security following     on behalf of the
February 2, 2000          made                   Exchange                such exchange          Company
<S>                      <C>                     <C>                     <C>                   <C>
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 $1,000,000,000
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</TABLE>


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