A method is provided for inhibiting corrosion in a layer of Cu or other material in a GMR sensor, wherein the GMR sensor may be used in a magnetic data storage system such as a tape drive system to substantially improve read head sensitivity. The GMR sensor comprises stacked layers of ferromagnetic and non-magnetic materials. In one useful embodiment, a layer of Cu material is positioned between first and second layers of a specified ferromagnetic material, such as CoFe. Respective end surfaces of the Cu layer and first and second CoFe layers are initially located in substantially co-planar relationship with one another, in a common plane. The method further comprises etching the Cu layer to remove an amount of material therefrom. A new end surface is thus formed in the Cu layer, wherein the new end surface is selectively spaced apart from the common plane. A protective coating is then applied to the new end surface of the Cu layer, to inhibit corrosion of such layer. Usefully, a pole tip recession is formed at the ends of the first and second CoFe layers.