This paper presents the cross-focusing of two intense laser beams in a collisionless plasma, taking into account the relativistic non-linearity. The non-linearity is not bound to large irradiances and this non-linearity is only a perturbation. It should be noted here that while considering the self-focusing due to relativistic electron mass variation, the electron ponderomotive density depression in the channel may also be important. Therefore, these two non-linearities may simultaneously affect the self-focusing process. In the present paper we have considered the situation when only relativistic non-linearity is important. The non-linearity due to relativistic mass variation depends not only on the intensity of one laser but also on the second laser. Therefore, one laser beam affects the dynamics of the second beam and hence a cross-focusing process takes place. The electric field amplitude of the excited electron plasma wave (EPW) has been calculated and its effect on the cross-focusing process has also been discussed. It is observed that the inclusion of a resonantly excited EPW on cross-focusing is significant and the accelerating electric field of the generated EPW becomes affected. A comparison of the theory with the recent experimental observations has also been presented.