Uniform ultimate boundedness of a class of switched linear systems is studied. A switched linear system in this class consists of m subsystems, and none of the individual subsystems need to be stabilizable. The switched linear system is shown to be uniformly ultimately bounded for any pre-given bound if the union of individual controllable subspaces covers the entire state space. An algorithm for guaranteeing uniform ultimate boundedness is given to provide the design of continuous controllers and the switching strategy.