The Milner-Shelah transversal theorem states, that if G=(A,B,E) is a (possibly infinite) bipartite graph such that there is no isolated vertex in A and for every edge {a,b} in E with a in A and b in B, d(a) >= d(b), then G admits a matching covering A. We provide a new proof of this theorem with a slight strengthening for finite graphs. (Joint work with Ron Aharoni)