Fe/Mn is a model system in which to study exchange bias, since the antiferromagnetic (AF) Mn layers are believed to have uncompensated moments with all spins aligned in the plane and parallel to those of the Fe. We have determined the microscopic AF ordering at the interfaces using single-crystal neutron diffraction. An unexpected magnetic structure is obtained, with out-of-plane Mn moments perpendicular to those of Fe. This explains the low bias field and shows that the simple AF ordering assumed in a variety of exchange-biased systems may well have to be revised.