Aizerman's method is a technique for investigating the asymptotic stability of a large class of autonomous feedback systems with one or more memoryless non-linear elements. Using an initial linearization, the method yields sectors to which the input-output characteristics of the non-linearity must be restricted in order to assure asymptotic stability in the large. Through a series of transformations a method for determining the sector of stability which is directly amenable to machine computation is presented in this paper.