Contrary to what many believe, stars and black holes do not remain stationary as objects revolve around them. While the Earth is revolving around the sun, the entire solar system is actually turning around its center of mass. Since the sun has much more mass than the planets, the sun's movement is barely noticeable.
So a black hole is just an incredibly massive thing, and assuming the other, even more massive object doesn't collapse in on itself due to gravity, both would rotate around the center of mass of the system.