The transverse non-specular magneto-optical Kerr effect was measured in diffraction from an inhomogeneous grating made of ferromagnetic Fe0.75Si0.25 wires on a silicon substrate. The relative change in intensity of the diffracted beams when magnetisation is reversed (Delta I/I)(n) shows a large enhancement (from 1.8 x 10(-2) up to 3 x 10(-1)) for angles of incidence corresponding to minima of I-n. The relative magnetic response, Delta D-n, where D-n is the diffraction efficiency (I-n/I-inc), reaches maximum values for non-zero diffracted orders and is higher than that obtained in specular conditions. (C) 1998 Elsevier Science B.V. All rights reserved.