  Given a compact Riemann surface $X$ and a moduli space $M_{\alpha}(\Lambda)$
of parabolic stable bundles on it of fixed determinant of complete parabolic
flags, we prove that the Poincar\'e parabolic bundle on $X\times
M_{\alpha}(\Lambda)$ is parabolic stable with respect to a natural polarization
on $X\times M_{\alpha}(\Lambda)$.
