We report the observation of unusual magnetic anisotropies in epitaxially grown Fe layers on PtMn films. The antiferromagnetic PtMn film has a twinned structure with crystallites of 8 nm. Each single PtMn grain is chemically ordered and exhibits a twofold magnetocrystalline anisotropy with an uncompensated surface magnetization. The bilayers display hysteresis with a complex dependence on applied field angle. A three vector model predicts the angular dependence of the hysteresis loops (shift and shape) of the Fe film and gives a detailed understanding of the Fe and antiferromagnet spin orientations during reversal. The interface exchange coupling between the Fe and the uncoupled PtMn twins accounts for the asymmetric magnetization reversal and high order anisotropies.