A graph is h-matchable if G-X has a perfect matching for every subset X ~ V(G) with IXI = h, and it is h-extendable if every matching of h edges can be extended to a perfect matching. It is proved that a graph G with even order is 2h-matchable if and only if (1) G is h-extendable; and (2) for any edge set D such that, for each e = xy E D, x,y E V(G) and e ~ E( G), G U D is h-extendable. Also ni...