  Earlier a magnetic anisotropy for magnetic impurities nearby the surface of
non-magnetic host was proposed in order to explain the size dependence of the
Kondo effect in dilute magnetic alloys. Recently Giordano has measured the
magnetoresistance of dilute Au(Fe) films for different thicknesses well above
the Kondo temperature $T_K$. In this way he verified the existence of that
anisotropy even for such a case where the Kondo effect is not dominating. For
detailed comparison of that suggestion with experiments, the magnetic field
dependence of the magnetoresistance is calculated in the lowest approximation,
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.
