Suppress Duplicates In Join Results

I really must be missing something here...

Trying to cross-update 2 tables.
Picture a checkbook reconcilliation without common check numbers. The checkbook has uniqueids and the bank has transaction ids but they are different. So the match is on date/payee and amount. So I wrote 2 checks to the same person, on the same day, for the same amount but forgot to enter one in the register.

when i run the update statement:
update b set b.bankid=c.myid
from checks c
join bank b on c.cdate=b.cdate
and c.payee=b.payee
and c.cost=b.cost

Both bank statement records would be updated to my one check record [can't happen]
Also: this will be running on a hundred thousand records per month with potential for duplication/ommission on either side.

What's a poor newbie missing??
I'm doing something similar on a lesser volume by running sequential statements through an ASP script but performance is poor. I know SQL can do this, just not how to approach it.

Thanks for any guidance
Dale