We have studied the magnetic-dipole and electric-quadrupole contributions to second-harmonic generation (SHG) of centro-symmetric media. It can be shown that the phenomenological parameters α, β, γ can be arranged to form an effective $$\bar \chi _s^{(2)} $$ -tensor, which describes dipole-forbidden SHG as the effect of a surface layer upon excitation with a single plane electromagnetic wave. An experimental technique is proposed allowing a determination of the usually very small γ term due to magnetic-dipole interaction using coherent compensation of its contribution by a coverage with an appropriate dye monolayer.