  In this paper, we consider a compact Kahler manifold with extremal Kahler
metric and a Mumford stable holomorphic bundle over it. We proved that, if the
holomorphic vector field defining the extremal Kahler metric is liftable to the
bundle and if the bundle is relatively stable with respect to the action of
automorphisms of the manifold, then there exist extremal Kahler metrics on the
projectivization of the dual vector bundle.
