  We discuss in this paper the conformal geometry of bi-invariant metrics on
compact semisimple Lie groups. For this purpose we develop a conformal Cartan
calculus adapted to this problem. In particular, we derive an explicit formula
for the holonomy algebra of the normal conformal Cartan connection of a
bi-invariant metric. As an example, we apply this calculus to the group
$\SO(4)$. Its conformal holonomy group is calculated to be $\SO(7)$.
