  Let $X$ be an irreducible smooth complex projective curve of genus at least
two. Let $N$ be a connected component of the moduli space of semistable
principal ${\rm PGL}_r({\mathbb C})$- bundles over $X$; it is a normal
unirational complex projective variety. We prove that the Brauer group of a
desingularization of $N$ is trivial.
