When electrons are confined to nanostructures, quantum interference takes place due to their wave-particle duality. Using spin-polarized scanning tunneling microscopy, we studied the influence of quantum interference of electrons on the spatial distribution of the spin polarization within a single magnetic nanostructure. We find changes in both the magnitude and sign of the spin polarization on a subnanometer scale. We compare our experimental results with <I>ab initio</I> calculations of the spin-resolved local density of states (LDOS). We find that the modulation of the spin-polarization at a given energy can be ascribed to the different magnitudes of spatially modulated majority states and non-modulated minority states contributing to the total LDOS.