If you aren't part of a workgroup (per '69 Camaro's response):
1) Open Access (with no database)
2) File>Open
3) Browse to the database file you want to remove the password from
4) !! Don't just click "Open"!! Click the arrow beside "Open" and select
"Open Exclusive"
5) After the file opens (and you have provided the password):
Tools>Security>"Unset Database Password"
Setting/unsetting a mdb password required that the file be opened
exclusively and the default status is "shared", even if you are the only one
in the file.