In this paper we give an explicit combinatorial description of the
maximal singular locus maxsing(X_w) of a Schubert variety X_w for an
element w \in S_n. With our description, the computation of
maxsing(X_w) becomes computationally efficient (O(n^6)). The key to
our result is a map R(y,w) --> R(yt,w) where yt < y < w, t is a
reflection, and R(y,w) is the set of reflections t' such that
y < yt' \leq w. Our result depends on a characterization
of maxsing(X_w) in terms of the cardinality of R(y,w) due to
Lakshmibai and Seshadri.
