Help Constructing Update Satement

I am almost a complete newbie to the UPDATE statement. I have a SQL Server 2005 instance with two databases.  I'll call one Hawk and one Eagle.  Hawk has a table called HawkInfo.  DDL Is as follows. 

CREATE TABLE HAWKINFO
(ARNumber NVARCHAR(255) NULL,
CSNUMBER NVARCHAR(12) NULL,
Customername NVARCHAR (12) NULL
)

There are 1215 rows out of some 26,000 that have a NULL CSNUMBER value.  I need to UPDATE the table, supplying the CSNUMBER where it is currently NULL.  There is a table in the EAGLE database called CUSTOMER that has the data I need.  DDL is as follows.

CREATE TABLE CUSTOMER
(ACCTID NVARCHAR (24) NULL,
CSNUMBER NVARCHAR(12) NULL
)

I can write the SELECT statement that retrieves the data that will be used to update the HAWKINFO table. It looks like this:

SELECT H.ARNUMBER
,C.CSNUMBER

FROM HAWKINFO H
INNER JOIN CUSTOMER C ON C.ACCTID = H.ARNUMBER
WHERE H.CSNUMBER IS NULL

How do I put this all together into an update statement that takes the CSNumber from Customer and update the NULL CSNumber values in HAWKINFO?

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Lee Markum