Spin-dependent scanning tunneling spectroscopy has been performed on single Co islands on Cu(111) at 7 K in fields of up to 4 T. The differential conductance shows a hysteretic behavior as a function of magnetic field. Symmetric hysteresis curves of the differential conductance are obtained which identify an abrupt switching of the Co island magnetization along the sample normal at fields around 1.5 T, and a reversible change of the spin orientation of the Cr-tip apex with increasing magnetic field. Our result allows a clear-cut assignment of the differential conductance curves in terms of parallel and antiparallel states of the spin orientation between tip and sample.