Let a non-negative real matrix Q be doubly stochastic,and a permutation matrix be a(0,1)-matrix which has exactly one 1 in each row and each column,then every permutation matrix will be doubly stochastic matrix.G.Birkhoff proved a conclusion that every doubly stochastic matrix Q can be expressed as a convex linear combination of permutation matrixs using the method of algerbra.Let G be a bipartite graph with bipartition(X,Y),then G contains a matching M that saturates every vertex in X if and only if d_G(S)≥|S| for all S⊆X.In this paper,we obtain the proof of graph theory on the conclusion using the above matching theorem of bipartite graph.