  We first exploit the spin symmetry relation $f^{\rm xc}_{s\bar s}
(\zeta)=f^{\rm xc}_{\bar s s}(-\zeta)$ for the exact exchange correlation
kernel $f^{\rm xc}_{s\bar s}(\zeta)$ in an inhomogeneous many electron system
with arbitrary spin polarization $\zeta$. The physical condition required to
satisfy the specific symmetry relation $f^{\rm xc}_{s\bar s}(\zeta) = f^{\rm
xc}_{\bar s s}(\zeta)$ is derived and examined for simple
ferromagnetic-nonmagnetic structure by taking the electrochemical potential
into account. The condition is then applied to several composite systems useful
in spintronics applications such as the magnetic system with net spin
polarization.
