Reduced dimensionality and symmetry breaking at interfaces lead to unusual local magnetic configurations, such as glassy behavior, frustration or increased anisotropy. The interface between a ferromagnet and an antiferromagnet is such an example for enhanced symmetry breaking. Here we present detailed X-ray magnetic circular dichroism and X-ray resonant magnetic reflectometry investigations on the spectroscopic nature of uncompensated pinned magnetic moments in the antiferromagnetic layer of a typical exchange bias system. Unexpectedly, the pinned moments exhibit nearly pure orbital moment character. This strong orbital pinning mechanism has not been observed so far and is not discussed in literature regarding any theory for local magnetocrystalline anisotropy energies in magnetic systems. To verify this new phenomenon we investigated the effect at different temperatures. We provide a simple model discussing the observed pure orbital moments, based on rotatable spin magnetic moments and pinned orbital moments on the same atom. This unexpected observation leads to a concept for a new type of anisotropy energy.