The exchange bias effect, especially the angular dependence of the exchange bias field and the coercivity of the epitaxial Ni81Fe19 /Fe50Mn50 bilayer system is investigated. In order to prepare a well defined layer sequence large emphasis is laid on the structural characterization of each layer. Low-energy electron diffraction and scanning tunneling microscopy are employed after each deposition step and the height-height-correlation function is analyzed to quantify the interface quality. Successively the angular dependence of the longitudinal and transverse magnetic component is investigated by magneto-optic Kerr effect magnetometry. In order to fully analyze the magnetization reversal behavior a special gray scale representation of the data is chosen. Theoretical results based on a modified Stoner-Wohlfarth model, which includes unidirectional and fourfold anisotropy contributions, are presented and compared to the experimental results. Although a homogeneous rotation of the magnetization is assumed the agreement between theory and experiment is surprisingly good. Only in a narrow angular range, where an ongoing rotation of the magnetization is predicted by the StonerWohlfarth theory, discrepancies arise. The angular dependence of the possible orientations of the magnetization are summarized in a phase diagram.