It is well-known that the size effect occurs in a conducting plate if the penetration depth of the electromagnetic wave irradiating the sample is of the same order as the plate thickness. At unilateral excitation, the size effect manifests itself as an abrupt growth of the surface resistance of the plate. It takes place due to the drastic increase of the electric field inside the sample under the condition of its full transparency. The electric field becomes of the same order as the magnetic field, and the surface resistance of the sample increases correspondingly. In the present paper we show that even at small amplitudes Hi of an incident wave (which we call the "base" wave with a frequency of ui) as it cannot penetrate through the whole volume of a hard superconductor, one can, nevertheless, observe the size effect by means of another wave (the "assisting" wave with an amplitude Hi and a frequency of 012), propagating in the opposite direction. This effect stems from the nonlinearity of superconducting media and does not depend essentially on the peculiarities of the nonlinearity mechanism. When the penetration regions of both waves overlap, the nonlinearity results in the appearance of all combined harmonics of the waves at every point of the sample. In particular, there exists a signal on the first harmonics u>\. As a result, the surface resistance on the frequency w\ of the base wave being small without the assisting wave, increases drastically when the penetration regions overlap each other. In the present paper we have studied the dependence of the surface impedance on the first frequency u>\ vs the amplitude #2 of the second wave. All the calculations in this paper were performed within the framework of the critical state model. The described effect of the stimulated transparency of the superconducting plate when acted upon by the assisting wave was observed experimentally.