Let G be a graph and let F = {F 1 , F 2 F m } and H be a factorization and a subgraph of G, respectively. If H has exactly one edge in common with F i for all i, 1 i m, then we say thatF is orthogonal to H. Let g and f be two integer-valued functions defined on V(G) such thatg (x) f(x) for every x V(G). In this paper it is proved that for anym -matching M of an (mg + m - 1, mf - m + 1)-graph G, there exists a (g, f)-factorization of G orthogonal to M.