It is known that the closure of an arbitrary $K_{\mathbf{C}}$-orbit on a flag manifold is expressed as a product of a closed $K_{\mathbf{C}}$-orbit and a Schubert cell ([M2], [Sp]). We already applied this fact to the duality of orbits on flag manifolds ([GM]). We refine here this result and give its new applications to the study of domains arising from the duality.