Existence of xed point in orthogonal metric spaces has been initiated recently by Eshaghi and et al. [On orthogonal sets and Banach xed Point theorem, Fixed Point Theory, in press]. In this paper, we introduce the notion of the strongly orthogonal sets and prove a genuine generalization of Banach' xed point theorem and Walter's theorem. Also, we give an example showing that our main theorem is a real generalization of these xed point theorems.