  We investigate the Ruderman-Kittel-Kasuya-Yosida oscillations of the
itinerant carrier spin density in a system where those oscillations appear only
due to a finite distribution of a localized spin. The system represents a
half-infinite one-dimensional quantum wire with a magnetic impurity located at
its edge. In contrast to the conventional model of a point-like exchange
interaction the itinerant carrier spin density oscillations in this system
exist. We {\it analytically} demonstrate that when the radius of the exchange
interaction is less than the wave length of the itinerant carriers living on
the Fermi surface, the long range behavior of the oscillations is identical to
the one taking place in the zero radius limit of the same exchange interaction
but for an infinite one-dimensional quantum wire where, in comparison with the
original half-infinite system, the mass of the itinerant carriers is {\it
strongly} modified by the exchange interaction radius. On the basis of our
analysis we make a suggestion on directionality of surface
Ruderman-Kittel-Kasuya-Yosida interaction shown in recent experiments: we
believe that in general the anisotropy of the Ruderman-Kittel-Kasuya-Yosida
interaction could result not only from the anisotropy of the {\it Fermi
surface} of itinerant carriers but also from the anisotropy of the {\it spin
carrying atomic orbitals} of magnetic impurities.
