Thin films of cobalt were deposited on annealed CoO single crystal disks having surfaces parallel to (100) and (111) planes. The films were cooled to below the Ne´el temperature of CoO in a high magnetic field. The magnetization loop and the magnetic torque curves of the film deposited on the (111) plane of the CoO crystal, recorded below the Ne´el temperature of CoO, showed a unidirectional anisotropy due to the exchange interaction between the ferromagnetic film and the antiferromagnetic substrate. The anisotropy energy related to this coupling was found by two independent methods to be about 4×105erg/cm3. However, when the film surface was parallel to the (100) plane of the substrate only a slight coupling energy was detected.