In this paper we present an appreciable simplification of the proof of an important result of Barry Mazur. Let K be a finite extension of Q, with residue class field k. Let A be a d-dimensional Abelian variety over K with good ordinary reduction and let u be a twist matrix of A (the precise definition of u will be given in Section 1). Suppose L is a totally ramified &-extension of K and let M&A(L) be the intersection of the groups NKnlKA(Kn) h w ere KC K, CL and [K, : K] = p”. Then we have an exact sequence