SQL query-help needed!

Given MYSQL tables:
groups (groupid, groupname)
groupmembers (index, groupid, userid)

groupmembers contains pairs of groupid, userid
any userid can be paired with several groupid values
any groupid can be paired with several userid values

I need a query that will return all groups.groupname that a userid is NOT part of.
Tried this:
select distinct groups.groupname, groups.groupid
from groups, groupmembers
where groupmembers.userid='$userid'
and groupmembers.group<>groups.groupid

but it also returns groups that $userid is part of
Any idea how to do it?