Using a beam of xenon ions together with a suitable mask, a GMR stack is ion milled until a part of it, no more than about 0.1 microns thick, has been removed so that a pedestal, having sidewalls comprising a vertical section that includes all of the free layer, has been formed. This is followed by formation of the longitudinal bias and conductive lead layers in the usual way. Using xenon as the sputtering gas enables the point at which milling is terminated to be more precisely controlled.