  For a finite Coxeter group, a subword complex is a simplicial complex
associated with a pair (Q, \pi), where Q is a word in the alphabet of simple
reflections, $\pi$ is a group element. We discuss the transformations of such a
complex induced by braid moves of the word Q. We show that under certain
conditions, this transformation is a composition of edge subdivisions and
inverse edge subdivisions. In such a case, we describe how the H- and the
\gamma-polynomials change under this operation. This case includes all braid
moves for groups with simply-laced Coxeter diagrams.
