A bias-adjusted giant magnetoresistive (GMR) device includes a ferromagnetic reference layer, which has a magnetization that remains relatively fixed when a range of magnetic fields is applied, and a ferromagnetic switching layer, which has a magnetization that can be changed by applying a relatively small magnetic field. In MRAM applications, the switching layer stores data in the form of the particular orientation of its magnetization relative to the magnetization of the reference layer. At least one of the reference and switching layers is split into at least two ferromagnetic layers separated by one or more layers of a nonmagnetic conductor, such that the hysteresis curve of resistance versus applied magnetic field is substantially symmetric about zero applied magnetic field.