Magnetocrystalline anisotropy is essential in the physics of antiferromagnets and commonly treated as a constant, not depending on an external magnetic field. However, we demonstrate that in CoO the anisotropy should necessarily depend on the magnetic field, which is shown by the spin Hall magnetoresistance of the CoO $|$ Pt device. Below the N\'eel temperature CoO reveals a spin-flop transition at 240 K at 7.0 T, above which a hysteresis in the angular dependence of magnetoresistance unexpectedly persists up to 30 T. This behavior is shown to agree with the presence of the unquenched orbital momentum, which can play an important role in antiferromagnetic spintronics.
