The singular locus of a Schubert variety X_v is determined by its smoothness at the T-fixed points indexed by permutations u less than v under the Bruhat order. We construct an affine open neighborhood around each u in X_v, decompose it into a product of an affine variety with some affine space. We define a combinatorial relation on pairs of permutations called interval pattern embedding, generalizing the usual notion of pattern embedding. Finally, we show how the open neighborhoods associated with different pairs of u<v are related when interval embedding occurs. This helps us reformulate known results on singular locus of Schubert varieties.