Abstract: We report the suppression of the Hall effect in a mesoscopic Hall cross with a strong magnetic field only in the centre and vanishingly small outside, The local magnetic field is produced by placing Dy pillar on top of a structure with a high-mobility two-dimensional electron gas. The effect is found to be due to a sharp increase of the number of back-scattered and quasi-localised electron orbits. The possibility of localising electrons inside the magnetic inhomogeneity region is discussed. (C) 2002 Elsevier Science B.V. All rights reserved.