Abstract In this project, we study the results of Colao and Marino on the paper "krasnosnoslskii-Mann method for non-self mappings" to approximate fixed points of non-self, non-expansive mappings in a real Hilbert space with out involving the calculation of a projection or a retraction mapping. To this end, for a closed, convex and nonempty subset C of a Hilbert space H and a non-expansive mappings T : C ! H, We introduce a new search strategy for the coefficients fa n g by a n+1 = max f a n , h(x n+1 ) g , where h(x) := inf f l 0 : lx + (1 l)Tx 2 C g and we prove that the Krasnoselskii-Mann algorithm x n+1 = a n x n + (1 a is well defined for this particular choice of the sequence fa g. We also prove both weak and strong convergence results when C is a strictly convex set and T is an inward mapping. We then illustrate this results with a brief numerical examples. n n )Tx n