  We examine static spin susceptibilities $\chi_{\alpha\beta}({\bf q})$ of spin
components $S_{\alpha}$ and $S_{\beta}$ in the non-centrosymmetric tetragonal
system. These show anomalous momentum dependences like $\chi_{xx}({\bf
q})-\chi_{yy}({\bf q})\sim q_x^2-q_y^2$ and $\chi_{xy}({\bf q})+\chi_{yx}({\bf
q})\sim q_x q_y$, which vanish in centrosymmetric systems. The magnitudes of
the anomalous spin susceptibilities are enhanced by the on-site Coulomb
interaction, especially, around an ordering wave vector. The significant and
anomalous momentum dependences of these susceptibilities are explained by a
group theoretical analysis. As the direct probe of the anomalous spin
susceptibility, we propose a polarized neutron scattering experiment.
