This paper studies state feedback control of discrete event systems under partial observation. A control specification is assumed to be specified by a predicate on the state space. It has been proved that M-controllability is a necessary and sufficient condition for the existence of a state feedback controller which solves the control problem. However, the given predicate is not necessarily M-controllable. In this case, a state feedback controller is synthesized for its M-controllable subpredicate. This paper characterizes all M-controllable subpredicates of a given predicate. Using the characterization, an M-controllable subpredicate that is larger than the supremal strongly M-controllable subpredicate is obtained. So the obtained M-controllable subpredicate is a better approximation of the given predicate.