Earlier a magnetic anisotropy for magnetic impurities nearby the surface of
nonmagnetic host was proposed in order to explain the size dependence of t
he Kondo effect in dilute magnetic alloys. Recently Giordano has measured t
he magnetoresistance of dilute Au(Fe) films for different thicknesses well
above the Kondo temperature T-K. In this way he Verified the existence of t
hat anisotropy even for such a case where the Kondo effect is not dominatin
g. For detailed comparison of that suggestion with experiments, the magneti
c field dependence of the magnetoresistance is calculated in the lowest app
roximation, thus in the second order of the exchange coupling. The strength
of the anisotropy is very close to earlier estimates deduced from the size
dependence of the Kondo resistivity amplitude.