A patterned, synthetic, longitudinally exchange biased GMR sensor is provided which has a narrow effective trackwidth and reduced side reading. The advantageous properties of the sensor are obtained by satisfying a novel relationship between the magnetizations (M) of the ferromagnetic free layer (F1) and the ferromagnetic biasing layer (F2) which enables the optimal thicknesses of those layers to be determined for a wide range of ferromagnetic materials and exchange coupling materials. The relationship to be satisfied is M.sub.F2/M.sub.F1=(J.sub.s+J.sub.ex)/J.sub.s, where J.sub.s is the synthetic coupling energy between F1 and F2 and J.sub.ex is the exchange energy between F2 and an overlaying antiferromagnetic pinning layer. An alternative embodiment omits the overlaying antiferromagnetic pinning layer which causes the relationship to become M.sub.F2/M.sub.F1=1.