<PAGE>   1
                                                                     EXHIBIT 4.1


CUSIP: 832110 AG 5
NO.  001
$250,000,000


         [THIS NOTE 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 THEREOF. THIS NOTE MAY NOT BE EXCHANGED IN WHOLE OR IN PART FOR A NOTE
REGISTERED, AND NO TRANSFER OF THIS NOTE IN WHOLE OR IN PART MAY BE REGISTERED,
IN THE NAME OF ANY PERSON OTHER THAN SUCH DEPOSITARY OR A NOMINEE THEREOF,
EXCEPT IN THE LIMITED CIRCUMSTANCES DESCRIBED IN THE INDENTURE.

         THE DEPOSITORY TRUST COMPANY, A NEW YORK CORPORATION ("DTC"), SHALL ACT
AS THE DEPOSITARY WITH RESPECT TO THE NOTES UNTIL A SUCCESSOR SHALL BE APPOINTED
BY THE COMPANY. UNLESS THIS CERTIFICATE IS PRESENTED BY AN AUTHORIZED
REPRESENTATIVE OF 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 THEREIN.]*

                            SMITH INTERNATIONAL, INC.

                           6-3/4% SENIOR NOTE DUE 2011

         SMITH INTERNATIONAL, INC., a Delaware corporation (the "Company", which
term includes any successor corporation under the Indenture referred to on the
reverse hereof), for value received, hereby promises to pay to Cede & Co., or
registered assigns, at the office or agency of the Company in New York, New
York, the principal sum of Two Hundred and Fifty Million Dollars on February 15,
2011, in the coin or currency of the United States, and to pay interest,
semi-annually on February 15 and August 15 of each year, commencing August 15,
2001, on said principal sum at said office or agency, in like coin or currency,
at the rate per annum specified in the title of this Note, from the February 15
or the August 15, as the case may be, next preceding the date of this Note to
which interest has been paid or duly provided for, unless the date hereof is a
date to which interest has been paid or duly provided for, in which case from
the date of this Note, or unless no interest has been paid or duly provided for
on this Note, in which case from February 16, 2001, until payment of said
principal sum has been made or duly provided for, and to pay interest (including
post-petition interest in any proceeding under

--------
*Include only if this Note is issued in global form.


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any applicable bankruptcy laws) on overdue installments of interest (without
regard to any applicable grace period) and on overdue principal and premium, if
any, from time to time on demand at the rate per annum specified in the title of
this Note, in each case to the extent lawful; provided, however, that payment of
interest may be made at the option of the Company by check mailed to the address
of the Person entitled thereto as such address shall appear in the Security
Register unless this Note is a Global Security, in which case all payments
hereon shall be made by wire transfer. Notwithstanding the foregoing, if the
date hereof is after February 1 or August 1, as the case may be, and before the
following February 15 or August 15, this Note shall bear interest from such
February 15 or August 15; provided, however, that if the Company shall default
in the payment of interest due on such February 15 or August 15, then this Note
shall bear interest from the next preceding February 15 or August 15, to which
interest has been paid or duly provided for or, if no interest has been paid or
duly provided for on this Note, from February 16, 2001. The interest so payable
on any February 15 or August 15 will, subject to certain exceptions provided in
the Indenture referred to on the reverse hereof, be paid to the person in whose
name this Note is registered at the close of business on February 1 or August 1,
as the case may be, next preceding such February 15 or August 15, whether or not
such day is a Business Day.

         Reference is made to the further provisions of this Note set forth on
the reverse hereof. Such further provisions shall for all purposes have the same
effect as though fully set forth at this place.

         This Note shall not be valid or become obligatory for any purpose until
the certificate of authentication hereon shall have been manually signed by the
Trustee under the Indenture.

         IN WITNESS WHEREOF, Smith International, Inc. has caused this
instrument to be signed manually or by facsimile by its duly authorized officer
and has caused its corporate seal to be affixed hereunto or imprinted hereon.

Dated:

(SEAL)                                 SMITH INTERNATIONAL, INC.

                                       By:
                                         ---------------------------------------
                                       Name:  Margaret K. Dorman
                                       Title: Senior Vice President and Chief
                                              Financial Officer



Attest:


-------------------------------
Name:  Neal S. Sutton
Title: Senior Vice President -
       Administrative General Counsel and Secretary


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                          CERTIFICATE OF AUTHENTICATION


         This is one of the Securities of the series designated pursuant to the
within-mentioned Indenture.

                                       THE BANK OF NEW YORK, as Trustee


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

Date of Authentication:



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                                 REVERSE OF NOTE

                            SMITH INTERNATIONAL, INC.

                           6-3/4% SENIOR NOTE DUE 2011

         This Note is one of a duly authorized issue of debentures, notes, bonds
or other evidences of indebtedness of the Company (hereinafter called the
"Securities") of the series hereinafter specified, all issued or to be issued
under and pursuant to an indenture dated as of September 8, 1997 (herein called
the "Indenture"), duly executed and delivered by the Company and The Bank of New
York, as Trustee (herein called the "Trustee"), to which Indenture, all
indentures supplemental thereto and all resolutions of the Board of Directors
establishing the form or terms of any series of Securities, reference is hereby
made for a description of the rights, limitations of rights, obligations, duties
and immunities 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 (if any) at different rates, may be subject
to different redemption provisions (if any), may be subject to different
sinking, purchase or analogous funds (if any) and may otherwise vary as in the
Indenture provided. This Note is one of a series designated as the 6-3/4% Senior
Notes due 2011 (herein called "the Notes") of the Company, limited initially in
aggregate principal amount to $250,000,000, with the Company having the option
to issue additional Notes in an unlimited aggregate principal amount from time
to time after the original issuance of the Notes.

         Interest will be computed on the basis of a 360-day year of twelve
30-day months. The Company shall pay interest on overdue principal and, to the
extent lawful, on overdue installments of interest at the rate per annum borne
by this Note. If a payment date is not a Business Day as defined in the
Indenture at a place of payment, payment may be made at that place on the next
succeeding day that is a Business Day, and no interest shall accrue for the
intervening period.

         In case an Event of Default with respect to Notes, as defined in the
Indenture, shall have occurred and be continuing, the principal hereof and the
interest accrued hereon, if any, may be declared, and upon such declaration
shall become, due and payable, in the manner, with the effect and subject to the
conditions provided in the Indenture.

         The Indenture contains provisions which provide that the Company and
the Trustee may enter into one or more supplemental indentures amending the
Indenture and the Securities of any series with the consent of the Holders of at
least a majority in principal amount of the Outstanding Securities of each
series affected by such supplemental indenture, and the Holders of at least a
majority in principal amount of the Outstanding Securities of any series may
waive (a) any past default under the Indenture with respect to such series and
its consequences and (b) either past or future compliance by the Company with
any provision of Sections 10.4 to 10.8 of the Indenture; provided that, without
the consent of each Holder of the Securities of each series affected thereby, an
amendment or waiver, including a waiver of past defaults, may not: (i) change
the due date of the principal of, or any installment of principal of or interest
on, any Security, or reduce the principal amount thereof or the rate of interest
thereon or any premium


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<PAGE>   5

payable upon redemption thereof, or reduce the amount of the principal of any
Security that would be due and payable upon a declaration of the maturity
thereof pursuant to the Indenture, or change the place of payment where, or the
coin or Currency in which, any Security or any premium or the interest thereon
is denominated or payable (or, in the case of certain Securities which provide
for less than the entire principal amount thereof to be due and payable upon a
declaration of acceleration of the maturity thereof pursuant to the Indenture,
reduce the amount of principal payable upon such a declaration of acceleration
of the maturity thereof), or impair the right to institute suit for the
enforcement of any such payment on or after the due date thereof (or, in the
case of redemption, on or after the Redemption Date), (ii) reduce the percentage
of the principal amount of the Outstanding Securities of any series, the consent
of whose Holders is required for any such supplemental indenture, or the consent
of whose Holders is required for any waiver (of compliance with the aforesaid
provisions of the Indenture or defaults thereunder and their consequences)
provided for in the Indenture or (iii) modify any of the provisions of Section
5.13, Section 9.2 or Section 10.10 of the Indenture, except to increase any such
percentage or to provide that certain other provisions of the Indenture cannot
be modified or waived without the consent of the Holder of each Outstanding
Security affected thereby.

         It is also provided in the Indenture that, subject to certain
conditions, the Holders of at least a majority in principal amount of the
Outstanding Securities of any series may waive an existing default with respect
to the Securities of such series and its consequences, except a default in the
payment of principal of (or premium, if any) or interest on any Security of such
series or in respect of a covenant or provision of the Indenture which cannot be
modified or amended without the consent of the Holder of each Outstanding
Security of such series affected. Upon any such waiver, such default shall cease
to exist, and any Event of Default arising therefrom shall be deemed to have
been cured, for every purpose of the Indenture; but no such waiver shall extend
to any subsequent or other default or impair any right consequent thereto.

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

         The Notes are issuable initially in fully registered form, without
coupons, in denominations of $1,000 and any whole multiple thereof at the office
or agency of the Company in New York, New York, and in the manner and subject to
the limitations provided in the Indenture, but, without the payment of any
service charge, Notes may be exchanged for a like aggregate principal amount of
Notes of other authorized denominations.

         The Notes shall be redeemable, in whole or in part at any time, at the
option of the Company on any date (a "Redemption Date"), at a Redemption Price
equal to the greater of (i) 100% of the principal amount of the Notes to be
redeemed and (ii) the sum of the present values of the remaining scheduled
payments of the principal amount of the Notes to be redeemed and interest
thereon (exclusive of interest accrued to the Redemption Date) from the
Redemption Date to the respective scheduled payment dates discounted from their
respective scheduled payment dates to the Redemption Date on a semiannual basis
(assuming a 360-day year consisting of twelve 30-day months) at the Treasury
Rate (as hereinafter defined) plus 35 basis


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points, plus accrued and unpaid interest on the principal amount being redeemed
to such Redemption Date.

         "Comparable Treasury Issue" means the United States Treasury security
selected by the Quotation Agent as having a maturity comparable to the term
between the Redemption Date and the Stated Maturity of the principal of the
Notes (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 with the Remaining Life.

         "Comparable Treasury Price" means, with respect to any Redemption Date,
the average of three Reference Treasury Dealer Quotations for such Redemption
Date.

         "Quotation Agent" means the Reference Treasury Dealer appointed by the
Company.

         "Reference Treasury Dealer" means each of Merrill Lynch Government
Securities Inc., Chase Securities Inc. and Morgan Stanley & Co. Incorporated and
their respective successors; provided, however, that if any of the foregoing
shall cease to be a primary U.S. Government securities dealer in The City of New
York (a "Primary Treasury Dealer"), the Company shall substitute therefor
another Primary Treasury Dealer.

         "Reference Treasury Dealer Quotation" means, with respect to each
Reference Treasury Dealer and any Redemption Date, the average, as determined by
the Trustee, 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 Trustee by such Reference Treasury Dealer at 5:00 p.m., The City
of New York time, on the third Business Day preceding such Redemption Date.

         "Treasury Rate" means, with respect to any Redemption Date, (1) the
yield, under the heading which represents the average for the immediately
preceding week, appearing in the most recently published statistical release
designated "H.15 (519)" or any successor publication which is published weekly
by the Board of Governors of the Federal Reserve System and which establishes
yields on actively traded United States Treasury securities adjusted to constant
maturity under the caption "Treasury Constant Maturities," for the maturity
corresponding to the Comparable Treasury Issue (if no maturity is within three
months before or after the Stated Maturity of the principal of the Notes, yields
for the two published maturities most closely corresponding to the Comparable
Treasury Issue shall be determined, and the Treasury Rate shall be interpolated
or extrapolated from such yields on a straight-line basis, rounding to the
nearest month) or (2) if such release (or any successor release) is not
published during the week preceding the calculation date or does not contain
such yields, the rate per year equal to the semiannual equivalent yield to
maturity 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 the Redemption Date. The Treasury
Rate shall be calculated on the third Business Day preceding the Redemption
Date.


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         Upon due presentment for registration of transfer of this Note at the
office or agency of the Company in New York, New York, a new Note or Notes of
authorized denominations for an equal aggregate principal amount will be issued
to the transferee in exchange therefor, subject to the limitations provided in
the Indenture, without charge except for any tax or other governmental charge
imposed in connection therewith.

         The Company, the Trustee and any agent of the Company or the Trustee
may deem and treat the registered Holder hereof as the absolute owner of this
Note (whether or not this Note shall be overdue and notwithstanding any notation
of ownership or other writing hereon), for the purpose of receiving payment of,
or on account of, the principal hereof and, subject to the provisions hereof,
interest hereon, and for all other purposes, and neither the Company nor the
Trustee nor any agent of the Company or the Trustee shall be affected by any
notice to the contrary.

         No recourse under or upon any obligation, covenant or agreement of the
Company in the Indenture, any indenture supplemental thereto or in any Note, or
because of any indebtedness evidenced thereby, shall be had against any
incorporator, stockholder, officer or director, as such, past, present, or
future, of the Company or of any successor corporation, either directly or
through the Company or any successor corporation, under any rule of law, statute
or constitutional provision or by the enforcement of any assessment or by any
legal or equitable proceeding or otherwise, all such liability being expressly
waived and released by the acceptance hereof and as part of the consideration
for the issue hereof.

         This Note shall be governed by and construed in accordance with the
internal laws of the State of New York without regard to conflicts of laws
principles thereof.

         Terms used herein which are defined in the Indenture shall have the
respective meanings assigned thereto in the Indenture.





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                                   ASSIGNMENT


         FOR VALUE RECEIVED, the undersigned hereby sell(s), assign(s) and
transfer(s) unto

[PLEASE INSERT SOCIAL SECURITY
OR OTHER IDENTIFYING NUMBER OF ASSIGNEE]


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

[PLEASE PRINT OR TYPE NAME AND ADDRESS, INCLUDING ZIP CODE, OF ASSIGNEE]


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


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the within Note and all rights thereunder, hereby irrevocably constituting and
appointing such person attorney to transfer such Note on the books of the
Company, with full power of substitution in the premises.


Dated:
         ---------------------------------

Signature:
          --------------------------------

NOTICE:           The signature to this assignment must correspond with the name
                  as written upon the face of the within Note in every
                  particular without alteration or enlargement or any change
                  whatsoever.


Signature Guarantee:
                    -----------------------------------


                               SIGNATURE GUARANTEE

         Signatures must be guaranteed by an "eligible guarantor institution"
meeting the requirements of the registrar, which requirements include membership
or participation in the Security Transfer Agent Medallion Program ("STAMP") or
such other "signature guarantee program" as may be determined by the registrar
in addition to, or in substitution for, STAMP, all in accordance with the
Securities Exchange Act of 1934, as amended.


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