The purpose of this paper is to present an alternate to the proof given in [3] of the local convergence of Broyden's method. The result was stated there as a simple corollary of a Kantorovich-type theorem for the method. Here we allow ourselves to assume the existence of a root for the system of equations in question and as a result we are able to slightly relax the requirements on the partial derivatives of the system and greatly simplify the proof. We will confine the description of the method to bare essentials and refer the reader to [1] or [3] for more details.