In this paper screening phenomena in general binary ionic solutions are analyzed from an Ornstein-Zernike point of view. The modified mean spherical approximation (MMSA) closure relation for the direct correlation function [Varela , J. Chem. Phys. 109, 1930 (1998)] is generalized in order to allow the presence of several species in solution. This generalized approximation (GMMSA) explicitly accounts for specific interactions between ionic species and is seen to allow the prediction of the hypernetted chain calculated decay length of 1:z(z=1,...,4) electrolyte solutions, in terms of a mean interaction parameter. Particularly, for 1:1 electrolyte solutions the results of the GMMSA for the effective decay length are seen to recover the original MMSA ones, and they are compared to all the theoretical results which exist in literature.