Assume that (X; d) is a complete metric space and T : X ! X is a self map of X with the following property: There is a positive integer J and an M 2 [0; 1); so that for any couple x; y 2 X; minfd(T i (x); T i (y)) : i = 1; 2;:::Jg M d(x; y): The assumption of the well known Banach Contraction Theorem, is the case where J = 1: In this case it can be proved that T is uniformly continuous and has a xed point. In the general case where J > 1; T need not be continuous. However, the Generalized Banach Contraction Theorem states that even in this case T also has a xed point. We shall present a proof of this theorem, which is mainly of combinatorial nature.