How do I remove an object from one group?

How do I remove an object from a single one of the groups that it’s in? I’ve tried: 3D View header > Object > Group > “Remove Selected From Active Group”, but can’t figure out how it works. I’ve tried selecting the object I want to remove, and then one other object from the group (to make the group “active”?), but this seems to simply remove both objects from their group. How do you make a single group “active”, especially if each member is also a member of another group?

in the object menu, it lists the groups that the object is in. Click on the X to remove it from a group

Thank you daren. I thought that that X would delete the group!