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This chapter presents a method of continuation for calculating a Brouwer fixed point. The algorithm is modeled on a different proof of the Brouwer theorem. The Brouwer Fixed Point theorem guarantees the existence of a fixed point, a point x⁰ e , such that F(x⁰) = x⁰. The broad applicability of this theorem makes the associated numerical problem important, namely, the problem of giving a generally applicable algorithm for finding the fixed point. In a proof of Brouwer theorem presented in the chapter, the existence of a fixed point is reduced to the nonexistence of a retraction H of onto δ D.