We have computed the fourth virial coefficient of a binary mixture composed of hard spheres with equal contact diameters for like particles but unequal collision diameter for particles belonging to unlike species. The independent irreducible cluster integrals which contribute to the fourth Virial coefficient were evaluated numerically using the Monte Carlo method. The coexistence line relative to the fluid-fluid phase transition, calculated through the truncated virial expansion for small positive values of the non-additivity parameter, is found to be in good agreement with the Gibbs ensemble Monte Carlo results.