Let G be a graph with vertex set V(G) and edge set E(G); and let g and f be two nonnegative integer-valued functions de3ned on V(G) such that g(x)≤(x) for every vertex x of V(G). We use dG(x) to denote the degree of a vertex x of G. A graph G is called a (g; f)-graph if g(x) ≤G(x) ≤(x) for each x ∈ V(G). Then a spanning subgraph F of G is said to be a (g; f)-factor of G if F itself is a (g; f)-graph. A (g; f)-factorizationof G is a partitionof E(G) into edge disjoint (g; f)-factors. Let F={F1; F2; : : : ; Fm} be a factorizationof G and H be a subgraph of G with m edges. If Fi≤i≤m, has exactly one edge in common with H, we say that F is orthogonal to H. Inthis paper it is proved that every (mg + k;mf − k)-graph contains a subgraph R such that R has a (g; f)-factorizationorthogon al to a givensubgraph with k edges, where m and k are positive integers with 1≤k＜m and g(x)≥0. This result has been conjectured by YaninYan(Sci. China Ser. A 41(1) (1998) 48).