A current-perpendicular-to-the-plane spin-valve (CPP-SV) magnetoresistive sensor has an improved antiparallel (AP) pinned structure. The AP-pinned structure has two ferromagnetic layers separated by a nonmagnetic antiparallel coupling (APC) layer and with their magnetization directions oriented antiparallel. One of the ferromagnetic layers in the AP-pinned structure is the reference layer in contact with the CPP-SV sensor's nonmagnetic electrically conducting spacer layer. In the improved AP-pinned structure each of the ferromagnetic layers has a thickness greater than 30 .ANG., preferably greater than approximately 50 .ANG., and the APC layer is either Ru or Ir with a thickness less than 7 .ANG., preferably about 5 .ANG. or less. The ultrathin APC layer, especially if formed of iridium (Ir), provides significant coupling strength to allow the thick ferromagnetic layers to retain their magnetization directions in a stable antiparallel orientation.