The decay of the remanent magnetization of several thin films of CoCr has been studied using the extraordinary Hall effect as a probe of the component of the magnetization perpendicular to the plane of the films. Consistent with previous measurements of CoCr, the remanent magnetization decays quasilogarithmically with time after the removal of a saturating magnetic field. In the present work the effect of a magnetically soft keeper layer on the decay of the magnetization has been investigated. It is found that the keeper layer does not affect the remanent magnetization nor does it decrease the decay rate of the perpendicular magnetization. This result indicates that the soft keeper layer is not effective at screening the demagnetization field on a length scale relevant to the decay-producing fields.