Exchange anisotropy was first discovered in oxidised cobalt particles (Co-CoO) by Meiklejohn and Bean (1956). They observed a shift in the hysteresis curve along the field axis, a non-vanishing rotational hysteresis, and a unidirectional component in torque curves, after the sample was cooled in a saturating magnetic field. Later the effect was also found in other ferro-antiferromagnetic systems by Meiklejohn (1962). In this letter a shift in the hysteresis curve of CoCr films is presented. RF-sputtered CoCr films were cooled in a magnetic field of 17 kOe from room temperature to liquid-nitrogen and helium temperatures. The shift is approximately 100 Oe in the direction opposite to the cooling field. The antiferromagnetic regions that are thought to be concentrated on the column boundaries offer a new opening in the discussion on the reversal mechanism of CoCr films.