Document:

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                                                                     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 MAY NOT BE TRANSFERRED
EXCEPT AS A WHOLE BY THE DEPOSITARY TO A NOMINEE OF SUCH DEPOSITARY OR BY A
NOMINEE OF SUCH DEPOSITARY TO SUCH DEPOSITARY OR ANOTHER NOMINEE OF SUCH
DEPOSITARY OR BY SUCH DEPOSITARY OR ANY SUCH NOMINEE TO A SUCCESSOR OF SUCH
DEPOSITARY OR A NOMINEE OF SUCH SUCCESSOR.

THIS GLOBAL NOTE CONSTITUTES A LONGER TERM DEBT SECURITY ISSUED IN ACCORDANCE
WITH THE REGULATIONS MADE UNDER SECTION 4 OF THE BANKING ACT 1987. HCA - THE
HEALTHCARE COMPANY IS NOT AN AUTHORIZED INSTITUTION OR A EUROPEAN AUTHORIZED
INSTITUTION (AS SUCH TERMS ARE DEFINED IN THE BANKING ACT 1987 (EXEMPT
TRANSACTIONS) REGULATIONS 1997). REPAYMENT OF THE PRINCIPAL AND PAYMENT OF ANY
INTEREST OR PREMIUM IN CONNECTION WITH THIS NOTE HAVE NOT BEEN GUARANTEED.

                                                                Principal Amount

                            HCA - THE HEALTHCARE COMPANY          L.150,000,000

                               8.75% NOTE DUE 2010

                                   GLOBAL NOTE

ISIN: XS011985700-0

Common Code: 011985700

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<PAGE>   2

         HCA - The Healthcare Company, a corporation duly organized and existing
under the laws of the State of Delaware (herein called the "Company" or "HCA,"
which term includes any successor corporation under the Indenture hereinafter
referred to), for value received, hereby promises to pay to Bank One, NA, London
branch or its registered assigns or the common depositary for Euroclear and
Clearstream, Luxembourg (each defined herein) the principal amount of One
Hundred and Fifty Million Pounds Sterling (L.150,000,000) on November 1, 2010
(the "Maturity Date") and to pay interest on May 1 and November 1 (each, an
"Interest Payment Date") in each year, beginning on May 1, 2001, and at the
Maturity Date specified above on said principal amount, at the rate of 8.75% per
annum, from November 1, 2000 until payment of said principal amount has been
made or duly provided for. If interest is to be calculated for any period other
than from one scheduled interest payment date to the next interest payment date,
it will be calculated on the basis of the actual number of days elapsed from and
including the previous interest payment date or, if none, the date of issue,
divided by 365 (or, if any of the days elapsed fall in a leap year, by 366). The
interest so payable on any Interest Payment Date (other than at maturity) will
be paid to the Person in whose name this Global Note is registered at the close
of business on the fifteenth day of the month immediately preceding the month in
which such interest payment is due (a "Regular Record Date"), unless the Company
shall default in the payment of interest due on any such Interest Payment Date,
in which case such defaulted interest shall be paid to the Person in whose name
this Global Note is registered at the close of business on a date for the
payment of such defaulted interest established by notice to the registered
holders of the Notes not less than ten days preceding such date (a "Special
Record Date"). In any case where the date for any payment on the Notes is not a
Business Day, such payment shall be made on the next succeeding Business Day. A
Business Day is any day that is not a Saturday or Sunday and that is not a day
on which banking institutions are generally authorized or required by law or
executive order to close in The City of New York or London and, for any place of
payment outside of The City of New York and London, in such place of payment.

         Both principal of and interest on this Global Note are payable in
immediately available funds in pounds Sterling, which at the time of payment is
legal tender for the payment of public and private debts. Payments of principal
and interest will be made in London at the office of Bank One, NA, London branch
and in Luxembourg at the office of Credit Agricole Indosuez Luxembourg S.A., or
at such other office or agency of the Company or its paying agent as the Company
shall designate pursuant to the Indenture referred to elsewhere herein. If,
prior to the maturity of this Global Note, the United Kingdom adopts the euro as
its lawful currency in accordance with the Treaty establishing the European
Communities, as amended by the Treaty on European Union, this Global Note will
be redenominated into euro, and the regulations of the European Commission
relating to the euro shall apply hereto. The circumstances and consequences
described in this paragraph will not entitle HCA, the Trustee or any holder of
or beneficial owner of interests in this Global Note to redeem early, rescind,
or receive notice relating to, the Notes, or repudiate the terms of this Global
Note or the Indenture, raise any other defense or request any compensation
claim, nor will such circumstances and consequences affect any of the other
obligations of HCA hereunder or under the Indenture.

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         This Global Note is one of a duly authorized issue of debentures,
notes, bonds or other evidences of indebtedness of the Company (the
"Securities"), of the series hereinafter specified, issued or to be issued under
an Indenture dated as of December 16, 1993, as supplemented, as may be amended
by indentures supplemental thereto (the "Indenture"), duly executed and
delivered by the Company to Bank One Trust Company, NA, the successor to The
First National Bank of Chicago, as Trustee (the "Trustee"), to which Indenture
reference is hereby made for a description of the respective rights and duties
thereunder of the Trustee, the Company and the holders of the Securities. The
Securities may be issued in one or more series, which different series may be
issued in various aggregate principal amounts, may mature at different times,
may bear interest at different rates, may have different conversion prices (if
any), may be subject to different redemption provisions, may be subject to
different sinking, purchase or analogous funds, may be subject to different
covenants and Events of Default and may otherwise vary as in the Indenture
provided. This Global Note is a global security representing the entire
principal amount of a series of Securities designated "8.75% Notes due 2010"
(the "Notes") issued under the Indenture. Unless otherwise provided herein, all
terms used in this Global Note, which are defined in the Indenture, shall have
the meanings assigned to them in the Indenture.

         The Notes do not have a sinking fund.

         The Notes may be redeemed by the Company prior to maturity, as a whole
or in part at any time after November 1, 2003. The redemption price shall equal
the greater of (i) 100% of the principal amount of such Notes and (ii) as
determined by the Calculation Agent, the price at which the Gross Redemption
Yield on the outstanding principal amount of the Notes on the Reference Date is
equal to the Gross Redemption Yield (determined by reference to the
middle-market price) at 3:00 p.m. (London time) on that date on the Benchmark
Gilt, plus 50 basis points, in either case, plus accrued and unpaid interest on
the Notes up to, but excluding the date specified as the redemption date.

"Gross Redemption Yield"      means a yield calculated on the basis indicated by
                              the Joint Index and Classification Committee of
                              the Institute and Faculty of Actuaries as reported
                              in the Journal of the Institute of Actuaries, Vol.
                              105, Part 1, 1978, page 18 or on such other basis
                              as the Trustee may approve.

"Reference Date"              means the date which is the first dealing day in
                              London prior to the publication of the notice of
                              redemption referred to below.

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"Benchmark Gilt"              means the 5.75% Treasury Stock due December 7,
                              2009 or such other United Kingdom government stock
                              as the Calculation Agent may, with the advice of
                              three brokers and/or United Kingdom gilt-edged
                              market makers or such other three persons
                              operating in the United Kingdom gilt-edged market
                              as the Calculation Agent may determine from time
                              to time to be the most appropriate benchmark
                              United Kingdom government stock for the Notes.

"Calculation Agent"           means Deutsche Bank AG London or any successor
                              entity.

         The Company will give notice of any redemption between 30 and 60 days
preceding the redemption date to each holder of the Notes to be redeemed in
accordance with the notice provisions set forth herein.

         Unless the Company defaults in payment of the redemption price, on and
after the redemption date, interest will cease to accrue on the Notes or
portions called for redemption.

         In case an Event of Default with respect to the Notes shall have
occurred and be continuing, the principal hereof may be declared, and upon such
declaration shall become immediately due and payable, in the manner, with the
effect and subject to the conditions provided in the Indenture. The Indenture
provides that such declaration may in certain events be waived by the holders of
a majority in principal amount of the Notes then Outstanding.

         All payments of principal and interest in respect of the Notes will be
without deduction or withholding for or on account of any present or future
taxes, duties, assessments or other governmental charges of whatsoever nature
imposed, levied, collected, withheld or assessed by the United States or any
political subdivision or taxing authority of or in the United States, unless
such withholding or deduction is required by law.

         In the event such withholding or deduction is required by law, subject
to the limitations described below, HCA will pay as additional interest on the
Notes to the holder or beneficial owner of any Note who is a non-U.S. holder
such additional amounts ("Additional Amounts") as may be necessary in order that
every net payment by HCA or any paying agent of principal of or interest on the
Notes (including upon redemption), after deduction or withholding for or on
account of any present or future tax, duty, assessment or other governmental
charge imposed upon or as a result of such payment by the United States or any
political subdivision or taxing authority of or in the United States, will not
be less than the amount provided for in such Note to be then due and payable
before any such tax, duty, assessment or other governmental charge.

However, HCA's obligation to pay Additional Amounts shall not apply to:

(a)      any tax, duty, assessment or other governmental charge which would not
         have been so imposed but for:

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         (1)      the existence of any present or former connection between such
                  holder or beneficial owner (or between a fiduciary, settlor,
                  beneficiary, member or shareholder or other equity owner of,
                  or a person having a power over, such holder or beneficial
                  owner, if such holder or beneficial owner is an estate, a
                  trust, a limited liability company, a partnership, a
                  corporation or other entity) and the United States, including,
                  without limitation, such holder or beneficial owner (or such
                  fiduciary, settlor, beneficiary, member, shareholder or other
                  equity owner or person having such a power) being or having
                  been a citizen or resident or treated as a resident of the
                  United States or being or having been engaged in a trade or
                  business in the United States or being or having been present
                  in the United States or having had a permanent establishment
                  in the United States;

         (2)      the failure of such holder or beneficial owner to comply with
                  any requirement under United States tax laws and regulations
                  to establish entitlement to a partial or complete exemption
                  from such tax, duty, assessment or other governmental charge
                  (including, but not limited to, the requirement to provide
                  Internal Revenue Service Forms W-8BEN, Forms W-8ECI, or any
                  subsequent versions thereof or successor thereto); or

         (3)      such holder's or beneficial owner's present or former status
                  as a personal holding company or a foreign personal holding
                  company with respect to the United States, as a controlled
                  foreign corporation with respect to the United States, as a
                  passive foreign investment company with respect to the United
                  States, as a private foundation or other tax exempt
                  organization with respect to the United States or as a
                  corporation which accumulates earnings to avoid United States
                  federal income tax;

(b)      any tax, duty, assessment or other governmental charge imposed by
         reason of the holder or beneficial owner:

         (1)      owning or having owned, directly or indirectly, actually or
                  constructively, 10% or more of the total combined voting power
                  of all classes of HCA's stock,

         (2)      being a bank receiving interest described in section
                  881(c)(3)(A) of the Internal Revenue Code of 1986, as amended,
                  or

         (3)      being a controlled foreign corporation with respect to the
                  United States that is related to HCA by stock ownership;

(c)      any tax, duty, assessment or other governmental charge which would not
         have been so imposed but for the presentation by the holder or
         beneficial owner of such Note for payment on a date more than 30 days
         after the date on which such payment became due and payable or the date
         on which payment of the Note is duly provided for and notice is given
         to holders, whichever occurs later, except to the extent that the
         holder or beneficial owner would have been entitled to such additional
         amounts on presenting such Note on any date during such 30-day period;

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(d)      any estate, inheritance, gift, sales, transfer, personal property,
         wealth, interest equalization or similar tax, assessment or other
         governmental charge;

(e)      any tax, duty, assessment or other governmental charge which is payable
         otherwise than by withholding from payment of principal of or interest
         on such Note;

(f)      any tax, duty, assessment or other governmental charge which is payable
         by a holder that is not the beneficial owner of the Note, or a portion
         of the Note, or that is a fiduciary, partnership, limited liability
         company or other similar entity, but only to the extent that a
         beneficial owner, a beneficiary or settlor with respect to such
         fiduciary or member of such partnership, limited liability company or
         similar entity would not have been entitled to the payment of an
         additional amount had such beneficial owner, settlor, beneficiary or
         member received directly its beneficial or distributive share of the
         payment;

(g)      any tax, duty, assessment or other governmental charge required to be
         withheld by any paying agent from any payment of principal of or
         interest on any Note, if such payment can be made without such
         withholding by any other paying agent; or

(h)      any combination of items (a), (b), (c), (d), (e), (f) and (g).

         For purposes of this section, the holding of or the receipt of any
payment with respect to a Note will not constitute a connection (1) between the
holder or beneficial owner and the United States or (2) between a fiduciary,
settlor, beneficiary, member or shareholder or other equity owner of, or a
person having a power over, such holder or beneficial owner, if such holder or
beneficial owner is an estate, a trust, a limited liability company, a
partnership, a corporation or other entity, and the United States.

         For purposes of this section, "non-US holder" means a beneficial owner
of a Note who or which is not:

         -        a United States citizen or lawful permanent resident
         individual;

         -        a corporation or partnership created or organized in or under
         the laws of the United States or any State thereof (including the
         District of Columbia);

         -        an estate if its income is subject to United States federal
         income taxation regardless of its source; or

         -        a trust (1) that validly elects to be treated as a United
         States person for United States federal income tax purposes or (2) (a)
         the administration over which a U.S. court can exercise primary
         supervision and (b) all of the substantial decisions of which one or
         more United States persons has the authority to control.

         Any reference in this Global Note to principal or interest shall be
deemed to refer also to Additional Amounts which may be payable under the
aforementioned provisions.

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         HCA will pay all stamp and other duties, if any, which may be imposed
by the United States or any political subdivision thereof or taxing authority
therein with respect to the issuance of the Notes.

         Except as specifically provided herein, HCA will not be required to
make any payment with respect to any tax, duty, assessment or other governmental
charge imposed by any government or any political subdivision or taxing
authority of or in the United States.

         Unless previously redeemed or repurchased and cancelled, the Notes will
be payable at par, including Additional Amounts, if any, on November 1, 2010 or
such earlier date on which the applicable Notes shall be due and payable in
accordance with the terms and conditions of the applicable Notes. However, if
the maturity date of the Notes is not a Business Day, the Notes will be payable
on the next succeeding Business Day and no interest shall accrue for the period
from the maturity date to such payment date.

         The Notes may be redeemed at HCA's option, in whole but not in part at
a redemption price equal to 100% of the principal amount of the Notes to be
redeemed, together with interest accrued and unpaid to the date fixed for
redemption, at any time, on giving not less than 30 nor more than 60 days'
notice in accordance with the notice provisions below, which notice shall be
irrevocable, if:

(a)      HCA has or will become obliged to pay Additional Amounts as a result of
any change in or amendment to the laws, regulations or rulings of the United
States or any political subdivision or any taxing authority of or in the United
States affecting taxation, or any change in or amendment to an official
application, interpretation, administration or enforcement of such laws,
regulations or rulings, which change or amendment is announced or becomes
effective on or after November 1, 2000, or

(b)      any action shall have been taken by a taxing authority, or any action
has been brought in a court of competent jurisdiction, in the United States or
any political subdivision or taxing authority of or in the United States,
including any of those actions specified in (a) above, whether or not such
action was taken or brought with respect to HCA, or any change, clarification,
amendment, application or interpretation of such laws, regulations or rulings
shall be officially proposed, in any such case on or after the date of the
prospectus supplement, which results in a substantial likelihood that HCA will
be required to pay Additional Amounts on the next interest payment date.

         However, no such notice of redemption shall be given earlier than 90
days prior to the earliest date on which HCA would be, in the case of a
redemption for the reasons specified in (a) above, or there would be a
substantial likelihood that HCA would be, in the case of a redemption for the
reasons specified in (b) above, obligated to pay such Additional Amounts if a
payment in respect of the Notes were then due.

         Prior to the publication of any notice of redemption pursuant to this
section, HCA will deliver to the Trustee:

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<PAGE>   8

(1)      a certificate signed by one of HCA's duly authorized officers stating
         that is entitled to effect such redemption and setting forth a
         statement of facts showing that the conditions precedent to HCA's right
         so to redeem have occurred, and

(2)      a written opinion of independent legal counsel of recognized standing
         to the effect that HCA has or will become obligated to pay such
         Additional Amounts as a result of such change or amendment or that
         there is a substantial likelihood that HCA will be required to pay such
         Additional Amounts as a result of such action or proposed change,
         clarification, amendment, application or interpretation, as the case
         may be. Such notice, once delivered by HCA to the Trustee, will be
         irrevocable.

         This Global Note is registered in the name of a common depositary for
Clearstream Banking, societe anonyme, Luxembourg ("Clearstream, Luxembourg") and
Morgan Guaranty Trust Company of New York, Brussels Office, as operator of the
Euroclear system ("Euroclear"). Investors may hold book-entry interests in this
Global Note through organizations that participate, directly or indirectly, in
Clearstream, Luxembourg and/or Euroclear system. Book-entry interests in the
Notes and all transfers relating to the Notes will be reflected in the
book-entry records of Euroclear and Clearstream, Luxembourg.

         The policies of Clearstream, Luxembourg and Euroclear will govern
payments, transfers, exchange and other matters relating to the investor's
interest in securities held by them. HCA has no responsibility for any aspect of
the records kept by Clearstream, Luxembourg or Euroclear or any of their direct
or indirect participants. We also do not supervise these systems in any way.

         The Company will issue to the holders Notes in fully certificated
registered form, only if (1) it advises the Trustee in writing that the
depositary is no longer willing or able to discharge its responsibilities
properly, and the Trustee or the Company is unable to locate a qualified
successor within 90 days; (2) an Event of Default has occurred and is continuing
under the Indenture; or (3) the Company, at its option, elects to terminate the
book-entry system. If any of the three above events occurs, the Trustee will
reissue the Notes in fully certificated registered form and will recognize the
registered holders of the certificated Notes as holders under the Indenture.

         Except as provided in the immediately preceding paragraph, this Global
Note may not be transferred except as a whole by the depositary to a nominee of
such depositary or by a nominee of such depositary to such depositary or another
nominee of such depositary or by such depositary or any such nominee to a
successor of such depositary or a nominee of such successor.

         In the event individual certificates for the Notes are issued, the
holders of such Notes will be able to receive payment on the Notes and effect
transfers of the Notes at the offices of the Luxembourg paying agent and
transfer agent. Pursuant to an Agency Agreement dated October 25, 2000, the
Company has appointed Credit Agricole Indosuez Luxembourg S.A. as paying agent
and transfer agent in Luxembourg with respect to the Notes in individual
certificated form. As long as the Notes are listed on the Luxembourg Stock
Exchange, HCA will maintain a paying agent in Luxembourg.

                                      -8-
<PAGE>   9

         Pursuant to an Agency Agreement dated October 25, 2000, Bank One, NA,
London branch, has also been appointed as a paying agent and registrar.

         Unless and until the Company issues the Notes in fully certificated,
registered form, (1) holders will not be entitled to receive a certificate
representing the holders' interest in the Notes; (2) all references in this
Global Note to actions by holders will refer to actions taken by the depositary
upon instructions from their direct participants; and (3) all references in this
Global Note to payments and notices to holders will refer to payments and
notices to the depositary, as the registered holder of the Notes, for
distribution to holders in accordance with its policies and procedures.

         While the Notes are represented by this Global Note deposited with the
common depositary for Euroclear and Clearstream, Luxembourg, notices to holders
may be given by delivery to Clearstream, Luxembourg and Euroclear and such
notices shall be deemed to be given on the date of delivery to Clearstream,
Luxembourg and Euroclear. The Trustee will mail notices by first class mail,
postage prepaid, to each registered holder's last known address as it appears in
the security register that the Trustee maintains. The Trustee will only mail
these notices to the registered holder of the Notes, unless HCA reissues the
Notes to holders or holders' nominees in fully certificated form.

         In addition, if the Notes are listed on the Luxembourg Stock Exchange,
and the rules of the Luxembourg Stock Exchange require notice by publication,
the Trustee will publish notices regarding the Notes in a daily newspaper of
general circulation in Luxembourg. HCA expects that this newspaper will be the
Luxemburger Wort. If publication in Luxembourg is not practical, the Trustee
will publish these notices elsewhere in Europe. Published notices will be deemed
to have been given on the date they are published. If publication as described
above becomes impossible, then the Trustee may publish sufficient notice by
alternate means that approximate the terms and conditions described in this
paragraph.

         Under New York's statute of limitations, any legal action to enforce
HCA's payment obligations evidenced by the Notes must be commenced within six
years after payment is due. Thereafter HCA's payment obligations will generally
become unenforceable.

         The Company may from time to time, without notice to or the consent of
the registered holders of the Notes, create and issue further notes ranking
equally with the Notes in all respects (or in all respects other than the
payment of interest accruing prior to the issue date of such further notes or
except for the first payment of interest following the issue date of such
further notes). Such further notes may be consolidated and form a single series
with the Notes and have the same terms as to status, redemption or otherwise as
the Notes.

         Several banks and other financial institutions have provided the
Company with a $1.2 billion credit facility under a term loan agreement dated as
of March 13, 2000, as amended. The Company will be in default under the Notes if
a default occurs under that agreement (as it may be amended, modified, extended,
renewed or replaced from time to time) and that default results in an
acceleration of the maturity of the Company's indebtedness under that agreement.
A declaration of the acceleration of the maturity of the Notes for this reason
is subject to annulment

                                      -9-
<PAGE>   10

if the default that caused acceleration of the indebtedness under the term loan
agreement is cured or waived and the Trustee is given notice of the cure or
waiver within sixty (60) days of the declaration. The Company does not need the
consent of the holders of the Notes to enter into any amendment, modification,
extension, renewal or replacement of the term loan agreement. An acceleration of
the indebtedness under the term loan agreement will cease to constitute a
default following the time, if ever, as the Notes are rated Baa3 (or the
equivalent) or higher by Moody's and BBB- (or the equivalent) or higher by
Standard & Poor's. "Moody's" means Moody's Investors Service, Inc. and its
successors. "Standard & Poor's" means Standard and Poor's Ratings Services, a
division of The McGraw-Hill Companies, Inc., and its successors.

         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 to be
affected under the Indenture by the Company and the Trustee with the consent of
the holders of not less than a majority in principal amount of the Outstanding
Securities of each series to be affected. It is also provided in the Indenture
that, prior to any declaration accelerating the maturity of the Notes as a
series, the holders of a majority in aggregate principal amount of the
Securities of such series at the time Outstanding may, on behalf of the holders
of all of the Securities of such series, waive any past default with respect to
the Securities of such series under the Indenture and its consequences, except a
default in the payment of the principal of, or interest on, any of the
Securities of such series.

         No reference herein to the Indenture and no provision of this Global
Note or of the Indenture (including the Company's right to defease and discharge
the Notes pursuant to Article Four and Article Fourteen 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 Global Note at the
place, at the respective times, at the rate and in the coin or currency herein
prescribed.

         Prior to due presentment for registration of transfer of this Global
Note, the Company, the Trustee and any agent of the Company or the Trustee may
deem and treat the holder hereof as the absolute owner of this Global Note
(whether or not this Global Note shall be overdue and notwithstanding any
notation of ownership or other writing hereon), for the purpose of receiving
payment hereof or on account hereof (except as otherwise provided in the
Indenture), as herein provided, and for all other purposes, and neither the
Company nor the Trustee nor any Paying Agent nor any Security Registrar shall be
affected by any notice to the contrary. All payments made to or upon the order
of such holder shall, to the extent of the sum or sums paid, effectually satisfy
and discharge liability for moneys payable on this Global Note.

         None of the Company, the Trustee, any Paying Agent or the Security
Registrar will have any responsibility or liability for any aspect of the
records relating to or payments made on account of beneficial ownership
interests of this Global Note or for maintaining, supervising or reviewing any
records relating to such beneficial ownership interests.

         No recourse for the payment of the principal of, or interest on, this
Global Note, or for any claims based hereon or otherwise in respect hereof, and
no recourse under or upon any obligation, covenant or agreement of the Company
in the Indenture or any indenture

                                      -10-
<PAGE>   11

supplemental thereto, or in any Note, or because of the creation of any
indebtedness represented thereby, shall be had against any incorporator,
stockholder, officer or director, as such, past, present or future, of the
Company, whether by virtue of any assessment or penalty or otherwise, all such
liability being, by the acceptance hereof and as part of the consideration for
the issue hereof, expressly waived and released.

         Except as otherwise expressly provided in this Global Note, this Global
Note shall in all respects be entitled to all benefits, and subject to the same
terms and conditions, as definitive registered securities authenticated and
delivered under the Indenture.

         The Indenture and this Global Note shall be governed by and construed
in accordance with the laws of the State of New York.

         This Global Note shall not be valid or become obligatory for any
purpose until the certificate of authentication hereon shall have been signed by
the Trustee under the Indenture referred to on the reverse hereof.

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

Dated as of  November 1, 2000                   HCA - THE HEALTHCARE COMPANY

                                                By:     /s/ David G. Anderson
                                                        ------------------------
                                                Title:  Senior Vice President-
                                                        Finance and Treasurer

                                                Attest: /s/ John M. Franck II
                                                        ------------------------
                                                Title:  Secretary

TRUSTEE'S CERTIFICATE
OF AUTHENTICATION

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

BANK ONE TRUST COMPANY, NA
as Trustee

By:    /s/ Jason Landless
       --------------------------------

Title: Assistant Vice President
       --------------------------------

                                      -11-<PAGE>   1
                                                                    Exhibit 10.1

                          HCA - THE HEALTHCARE COMPANY

                                       AND

                           BANK ONE, NA, LONDON BRANCH
                          AS PAYING AGENT AND REGISTRAR

                                       AND

                    CREDIT AGRICOLE INDOSUEZ LUXEMBOURG S.A.
                       AS PAYING AGENT AND TRANSFER AGENT

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

                     AGENCY AGREEMENT (8.75% NOTES DUE 2010)
                          DATED AS OF OCTOBER 25, 2000

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

<PAGE>   2

THIS AGREEMENT is made in London as of October 25, 2000 AMONG

(1)      HCA - THE HEALTHCARE COMPANY (the "ISSUER"),

(2)      BANK ONE, NA, LONDON BRANCH ("BANK ONE"), which shall act as paying
         agent and registrar (hereinafter referred to in such respective
         capacities as "PAYING AGENT" or "REGISTRAR," which expressions shall
         include any successor or successors thereto), and

(3)      CREDIT AGRICOLE INDOSUEZ LUXEMBOURG S.A., ("Credit Agricole") which
         shall act as paying agent and transfer agent (hereinafter referred to
         as "PAYING AGENT AND TRANSFER AGENT", which expression shall include
         any successor or successors thereto).

         WHEREAS, pursuant to the Underwriting Agreement Standard Provisions
(Debt Securities) dated October 25, 2000, which is incorporated into the
Underwriting Agreement (Terms) dated October 25, 2000, between the Issuer and
the Underwriters referred to therein (together, the "Underwriting Agreement"),
the Issuer has agreed to issue L.150,000,000 of its 8.75% Notes due 2010 (THE
"NOTES");

         WHEREAS the Issuer wishes to appoint Bank One to act as Paying Agent
and Registrar and Credit Agricole as Paying Agent and Transfer Agent in relation
to the Notes upon the terms and conditions set forth in this Agreement and the
Schedules hereto.

         IT IS HEREBY AGREED as follows:

1.       DEFINITIONS, INTERPRETATION

         The following terms shall, unless the context otherwise requires, have
the respective meanings indicated below:

         "AGENT(S)" means any of the Registrar, the Paying Agent or the Transfer
         Agent.

         "CONDITIONS" means the terms and conditions of the issue of the Notes,
         as contained in the Global Note, the Prospectus dated August 5, 1999,
         as supplemented by the Prospectus Supplement, dated October 25, 2000,
         the Officer's Certificate related to the issue of the Notes dated
         November 1, 2000 and the Indenture.

         "GLOBAL NOTE" means the Global Note in the form of Schedule 1 attached
         hereto.

         "INDENTURE" means the Indenture dated as of December 16, 1993, as
         supplemented on May 25, 2000 between the Issuer and Bank One Trust
         Company, NA, the successor of the First National Bank of Chicago, as
         Trustee (the "Trustee"), a copy of which is attached hereto as
         Schedule 2.

                                      -2-
<PAGE>   3

         Terms not defined herein shall have the same meanings as are assigned
         thereto in the Underwriting Agreement.

2.       APPOINTMENTS

2.1      The Issuer hereby appoints Bank One to act as Paying Agent and
Registrar in respect of the Notes and Global Note.

2.2      Bank One hereby accepts such appointment and the resulting obligations,
and agrees to act in such capacities, on the terms and conditions set out in
this Agreement and the Schedules hereto. In particular, the Paying Agent agrees
to effect any publication of notices pursuant to the Conditions.

2.3      The Issuer hereby appoints Credit Agricole to act as Paying Agent and
Transfer Agent in respect of the Notes and Global Note.

2.4      Credit Agricole hereby accepts such appointment and the resulting
obligations, and agrees to act in such capacities, on the terms and conditions
set out in this Agreement and the Schedules hereto.

2.5      The obligations of the Agents are several and not joint.

3.       THE NOTES

3.1      The Notes shall be represented by a permanent Global Note without
interest coupons as specified in the Conditions. The Global Note shall be
substantially in the form attached hereto as Schedule 1, in each case with such
changes as may be agreed between the Issuer and the Trustee. Individual Notes
shall not be issued.

3.2      Each Global Note shall be signed manually by a duly authorized officer
of the Issuer and dated November 1, 2000. Each Global Note shall be
authenticated manually by the Trustee and delivered to Bank One as common
depository for Euroclear System and Clearstream Banking, societe anonyme,
Luxembourg (hereinafter "Euroclear" and "Clearstream Luxembourg," respectively).

4.       PAYING AGENCY

4.1      The Issuer shall remit the funds necessary for the payment of interest
on and principal of the Notes to the Paying Agent, in pounds Sterling, in
same-day funds, to such account at the Paying Agent in London as the Paying
Agent may from time to time specify (the "REDEMPTION ACCOUNT") on the Business
Day such payment is due, provided always that, if any due date shall not be a
Business Day, the Issuer shall make such transfer to the account of the Paying
Agent on the next succeeding Business Day (for the purposes of the Agreement,
Business Day shall have the same definition as Business Day contained in the
Prospectus Supplement).

                                      -3-
<PAGE>   4

The Issuer hereby authorizes and directs the Paying Agent, from the amounts so
paid to, it to make payment of the principal of, and interest on, the Notes on
the due date for payment set forth in the Conditions and this Agreement. If
applicable, the Paying Agent will, from funds so received from the Issuer,
credit to the account of the Paying Agent the amounts of all such payments made
by it in accordance with the provisions of this Agreement.

The Issuer understands that it should confirm to the Paying Agent not later than
10:00 a.m. (London time) on the second Business Day before the relevant date for
such payment that it has issued irrevocable payment instructions for such
payment to be made. The Paying Agent shall contact the Issuer not later than ten
Business Days before the respective due date with regard to such payment. The
Redemption Account shall be free of charge.

4.2      If for any reason (other than negligence or willful misconduct on the
part of the Paying Agent or its officers, employees or agents) the Paying Agent
does not receive unconditionally the full amount payable by the Issuer on the
relevant due date in respect of all the outstanding or maturing Notes, the
Paying Agent shall forthwith notify immediately the Issuer by telephone followed
by facsimile and the Paying Agent shall not be bound to make any payment of
principal or interest in respect of the Notes until the Paying Agent has
received to its order the full amount of the moneys then due and payable in
respect of all outstanding or maturing Notes, provided, however, that if the
Paying Agent shall, in its discretion, make any payment of principal or interest
on or after the due date therefor in respect of the Notes prior to its
unconditional receipt of the full amount then due and payable in respect of all
outstanding Notes, the Issuer will promptly pay such amount to the Paying Agent
and will compensate the Paying Agent at a rate equal to the Paying Agent's cost
of funding.

4.3      Out of the sums paid to the Paying Agent in respect of interest and
principal on the Notes, the Paying Agent will make payment free of charge to the
registered holder of the Global Note as stipulated in Clause 8 below, in the
amounts specified in the Conditions. The Paying Agent shall obtain from the
Registrar, and the Registrar shall supply, such details as are required for the
Paying Agent to make payment as stated above.

4.4      In respect of the monies paid to it relating to any Note, the Paying
Agent

         4.4.1    shall not be entitled to exercise any lien, right of set-off
                  or similar claim (including without limitation any claim
                  arising from or relating to any other issue of securities by
                  the Issuer),

         4.4.2    shall not be required to account for interest thereon, and

         4.4.3    need not segregate money held by it, except as required by
                  law.

5.       DOCUMENTS FOR INSPECTION AND PUBLICATION OF NOTICES

5.1      On behalf and at the request and expense of the Issuer, the Paying
Agent shall cause to be published any notices required to be given by the Issuer
in accordance with the Conditions.

                                      -4-
<PAGE>   5

5.2      The Issuer shall provide to the Paying Agent sufficient copies of all
documents required by the Conditions to be available for issue or inspection,
and the Paying Agent shall make such copies available to the holders of the
Notes upon their request.

5.3      To the extent practicable, the Issuer shall provide the Paying Agent
with a copy (prior to publication) of all notices to be issued in connection
with the Notes.

6.       CANCELLATION OF THE GLOBAL NOTE

6.1      Subject to the terms of the Indenture, promptly upon the Issuer's
request, the Registrar shall take all measures necessary to cancel any Notes
which the Issuer has repurchased or whose maturity has been accelerated pursuant
to the Conditions. The Registrar shall cause any such Notes to be canceled,
resulting in a reduction in the aggregate amount of the Notes represented by the
Global Note by the aggregate amount of Notes so canceled.

6.2      On the same day such cancellation is effected, the Registrar shall
record such cancellation of Notes on the Register, as defined below, in such a
way that the aggregate principal amount of Notes canceled at any time together
with the aggregate principal amount of Notes outstanding and represented by the
Global Note shall equal the aggregate principal amount of Notes originally
issued by the Issuer.

6.3      The Registrar shall upon request furnish the Issuer with a notice of
cancellation signed by an authorized officer of the Registrar confirming the
cancellation of such Notes and the corresponding reduction of the relevant
Global Note.

7.       DUTIES OF THE REGISTRAR

7.1      The Registrar shall maintain a register (the "Register") in London in
accordance with the Conditions. The Register shall show the aggregate amount of
Notes represented by each Global Note at the date of issue and all subsequent
transfers and exchanges involving a change in such amounts and the names and
addresses of the registered holders (each a "PAYEE"). On the first Business Day
after the Record Date for any interest payment on the Notes, the Registrar shall
send payment details in respect of the Payees and the accounts to which
transfers should be made to the Paying Agent.

7.2      Transfers or exchanges of Notes will be made in accordance with the
Conditions, the procedures established for this purpose between Euroclear,
Clearstream, Luxembourg, and the Registrar, and the regulations of Euroclear and
Clearstream, Luxembourg applicable to such transfers or exchanges. Any such
transfer or exchange which results in a change in the aggregate principal amount
of Notes held by Euroclear and Clearstream, Luxembourg shall be notified by
Euroclear and Clearstream, Luxembourg to the Registrar. The Registrar shall
promptly enter details of the transfer or exchange in the Register, which entry
shall, without further action, cause the aggregate principal amount represented
by each Global Note to be amended accordingly.

7.3      The Registrar shall at all reasonable times during office hours make
the Register available to the Issuer and the Paying Agent or any person
authorized by either of them for inspection and

                                      -5-
<PAGE>   6

for the taking of copies thereof or extracts therefrom, and the Registrar shall
deliver to such persons such information contained in the Register or relating
to the Notes as they may reasonably request.

8.       DUTIES OF THE TRANSFER AGENT

If and to the extent so specified by the Conditions and in accordance therewith,
or if otherwise requested by the Issuer, the Transfer Agent shall make available
all relevant forms of transfer, inform the Registrar of the name and address of
the relevant person to be inserted in the Register and carry out such other acts
as may be necessary to give effect to the Conditions and this Agreement.

9.       CONDITIONS OF APPOINTMENT

9.1      The Issuer will pay to the Agents a remuneration for all services
rendered hereunder by the Agents in connection with the Notes, together with any
expenses incurred only to the extent separately agreed upon by the Agents and
the Issuer.

9.2      The Issuer will indemnify and hold harmless each of the Agents against
any loss, liability or expense which it may incur or any claim, action or demand
which may be made against it resulting from the negligence or willful misconduct
on the part of the Issuer (or its officers, employees or agents (other than the
Agents and their officers, employees, and agents)) and arising out of or in
connection with such Agent's appointment or the exercise of its powers and
duties hereunder without negligence or willful misconduct on the part of such
Agent.

9.3      Each Agent will indemnify and hold harmless the Issuer against any
loss, liability or expense incurred by the Issuer or any claim, action or demand
which may be made against the Issuer resulting from the negligence or willful
misconduct on the part of such Agent (or such Agent's officers, employees or
agents) and arising out of or in connection with such Agent's duties hereunder.

9.4      The indemnities above shall survive the termination or expiry of this
Agreement.

9.5      Each of the Agents shall be protected and shall incur no liability for
or in respect of any action taken, omitted or suffered in reliance upon any
instruction or communication from the Issuer or any document reasonably believed
by it to be genuine and to have been delivered, signed or sent by the proper
party or parties in accordance with the provisions hereof, except such as may
result from its own negligence or willful misconduct or that of its officers,
employees or agents.

9.6      In acting hereunder and in connection with the Notes, the Agents do not
assume any relationship of agency and trust for the holders of the Notes and
shall not have any obligation towards them except that all funds held by a
Paying Agent for payment of principal of or interest on the Notes shall be held
exclusively for the benefit of and for payment to the holders of the Notes and
shall be applied as set forth herein and in the Conditions.

                                      -6-
<PAGE>   7

9.7      Nothing herein shall be deemed to require any Agent to advance its own
funds in the performance of its duties hereunder.

9.8      The Agents may consult with legal and other professional advisers
selected in good faith and satisfactory to them and the advice or opinion of
such advisers shall be full and complete protection in respect of any action
taken, omitted or suffered hereunder in good faith and without negligence and in
accordance with the advice or opinion of such advisers.

9.9      The Agents shall be obliged to perform such duties and only such duties
as are herein specifically set forth, and no implied duties or obligations shall
be read into this Agreement against the Agent. No Agent shall be under any
obligation to take any action hereunder which it expects will result in any
expense or liability of such Agent, the payment of which within a reasonable
time is not, in its opinion, assured to it.

9.10     The Agents and their officers, employees and affiliates, in their
individual or any other capacity, may become the owner of, or acquire any
interest in, any Notes with the same rights that the Agents would have if they
were not the Agents hereunder.

10.      CHANGE IN AGENTS

10.1     Each of the Paying Agent and Registrar and Paying Agent and Transfer
Agent, in its capacity as such, may be removed at any time by the giving to it
of at least 30 days' written notice to that effect signed on behalf of the
Issuer specifying the date on which such removal shall become effective. Each of
the Paying Agent and Registrar and Paying Agent and Transfer Agent may at any
time resign by giving at least 30 days' written notice (unless the Issuer agrees
to accept less notice) to that effect to the Issuer specifying the date on which
such resignation shall become effective. Notwithstanding the foregoing, no such
resignation or removal shall take effect within 30 days before or after any due
date for payment of any Notes or before a new Paying Agent and Registrar and
Paying Agent and Transfer Agent, as the case may be, shall have been appointed
by the Issuer as hereinafter provided, and such new Agent shall have accepted
such appointment. Any change in any Agent shall be notified by the Issuer to the
other Agent(s).

10.2     The Issuer agrees with the Paying Agent that if, by the day falling 10
days before the expiry of any notice under Clause 10.1 above, the Issuer has not
appointed a replacement Paying Agent, then the Paying Agent shall be entitled,
on behalf of the Issuer, to appoint in its place any reputable financial
institution of good standing and the Issuer shall not unreasonably object to
such appointment.

10.3     Upon the effectiveness of the appointment of any successor Paying Agent
and Registrar or Paying Agent and Transfer Agent, as the case may be, pursuant
to Clause 10.1, the Paying Agent and Registrar or Paying Agent and Transfer
Agent so removed shall cease to be a Paying Agent and Registrar or Paying Agent
and Transfer Agent, as the case may be, hereunder. Prior to the effectiveness of
such appointment, the Paying Agent and Registrar or Paying Agent and Transfer
Agent shall transfer all moneys deposited with it or held by it hereunder in
respect of the Notes to the order of the respective successor Paying Agent and
Registrar or Paying Agent and Transfer Agent.

                                      -7-
<PAGE>   8

11.      NOTICES

         Notices shall be in writing (including by facsimile) and addressed to
the relevant party hereto as follows:

(a)      If to the Issuer:

         HCA - The Healthcare Company
         One Park Plaza
         Nashville, Tennessee 37203

         Telephone: +1 (615) 344-9551
         Telefax:   +1 (615) 344-2598

         Attn: John M. Franck II

(b)      If to the Paying Agent and Registrar

         Bank One, NA, London Branch
         27 Leadenhall Street
         London EC2A 1AA

         Telephone: 44-20-7903-4192
         Telefax:   44-20-7903-4547

         Attn: Corporate Trust

(c)      If to the Paying Agent and Transfer Agent:

         Credit Agricole Indosuez Luxembourg S.A.
         39 Allee Scheffer
         L-25250 Luxembourg

         Telephone: +352-47-67-2344
         Telefax:   +352-47-67-3344

         Attn: M. Gilson de Rouvreux

or at any other address of which any of the foregoing shall have notified the
others, and shall be deemed to have been given when received by the relevant
party.

12.      APPLICABLE LAW, PLACE OF JURISDICTION

12.1     This Agreement shall be governed by the laws of the State of New York,
without regard to its conflict of laws principles.

                                      -8-
<PAGE>   9

12.2     The non-exclusive place for all proceedings arising out of this
agreement shall be New York.

13.      MISCELLANEOUS

13.1     The Paying Agent shall promptly advise the Issuer of any notice,
including any notice declaring Notes due, which it may receive pursuant to the
Conditions.

13.2     Should any of the provisions of this Agreement be or become invalid, in
whole or in part, the other provisions of this Agreement shall remain in force.
Invalid provisions shall, according to the intent and purpose of this Agreement,
be replaced by such valid provisions which in their economic effect come as
close as legally possible to that of the invalid provisions.

13.3     This Agreement may be signed in one or more counterparts.

13.4     If there is any conflict between the terms of this Agreement and the
terms of the Indenture, the terms of the Indenture shall control.

13.5     The terms of the United States Trust Indenture Act of 1939, as amended
(the "Trust Indenture Act"), shall be incorporated by reference herein to the
extent applicable. Each of the Agents shall abide by the Trust Indenture Act, to
the extent applicable. Nothing in this agreement shall be deemed to conflict
with the Trust Indenture Act and, to the extent of any such conflict and to the
extent applicable, the terms of the Trust Indenture Act shall be deemed to
govern.

                                      -9-
<PAGE>   10

This Agreement has been entered into effective the date stated at the beginning
hereof.

HCA - THE HEALTHCARE COMPANY

By: /s/ David G. Anderson
    -----------------------------------------------

Print Name: David G. Anderson
            ---------------------------------------

Title:  Senior Vice President-Finance and Treasurer
        -------------------------------------------

BANK ONE, NA, LONDON BRANCH

By: /s/ Anna Hogg
    ----------------------------------------------

Print Name: Anna Hogg
            --------------------------------------

Title: Assistant Vice President
       -------------------------------------------

CREDIT AGRICOLE INDOSUEZ LUXEMBOURG S.A.

By: /s/ Anna Hogg
    ----------------------------------------------

Print Name: Anna Hogg
            --------------------------------------

Title: Assistant Vice President
       -------------------------------------------

                                      -10-
<PAGE>   11

                                   SCHEDULE 1

                                  [GLOBAL NOTE]

                                      -11-
<PAGE>   12

                                   SCHEDULE 2

                                   [INDENTURE]

                                      -12-

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