This paper studies M-controllable subpredicates of a given predicate, which arise in state feedback control of discrete event systems under partial observations. First, the notion of strong M-controllability of predicates, which is a stronger version of M-controllability, is introduced. Then it is shown that there always exists the supremal strongly M-controllable subpredicate of a given predicate. Also, it is proved that the supremal strongly M-controllable subpredicate is larger than the supremal controllable and normal subpredicate obtained by Li. However, the supremal strongly M-controllable subpredicate is not a maximal M-controllable subpredicate in general. A sufficient condition for an obtained M-controllable subpredicate to be a maximal one is presented.