  Let $H$ be a connected semisimple linear algebraic group defined over
$\mathbb C$ and $X$ a compact connected Riemann surface of genus at least
three. Let ${\mathcal M}'_X(H)$ be the moduli space parametrising all
topologically trivial stable principal $H$-bundles over $X$ whose automorphism
group coincides with the centre of $H$. It is a Zariski open dense subset of
the moduli space of stable principal $H$-bundles. We prove that there is a
universal principal $H$-bundle over $X\times {\mathcal M}'_X(H)$ if and only if
$H$ is an adjoint group (that is, the centre of $H$ is trivial).
