In this paper, we apply the concept of the group ulcorner(X,A) of self pair homotopy equivalences of a CW-pair (X, A) to the Postnikov system. By using a short exact sequence related to the group of self pair homotopy equivalences, we obtain the following result: for any Postnikov section X$sub$n/ of a CW-complex X, the group ulcorner(X$sub$n/, A) of self pair homotopy equivalences on the pair (X$sub$n/, X) is isomorphic to the group ulcorner(X) of self homotopy equivalences on X. As a corollary, we have, ulcorner(K($pi$, n), M($pi$, n)) ≡ ulcorner(M($pi$, n)) for each n$pi$1, where K($pi$,n) is an Eilenberg-Mclane space and M($pi$,n) is a Moore space.