Mine our housetrained. Max came that way. But when I was training Jake I would yell "Outside!" as soon as he looked like he was getting ready to go. That would startle him enough to make him stop. Then I'd bring him outside and praise him to high heaven when he went. If I didn't catch him, I would just clean it up and not say anything.

Max seems to think the basement is outside. I can see where he'd get confused - it's an old, damp basement. If I could heave ever caught him in the act I would have just run him outside. But - I couldn't. So we just put up a door so he can't get down there anymore.