Let D be a bounded symmetric domain. Let G be the universal covering group of the identity component A "(D) of the group of all holomorphic diffeomorphisms of D onto itself. In this case, any G-hotnogeneous vector bundle E -D admits a natural structure of G-homogeneous holomorphic vector bundles. The vector bundle E -D must be holomorphically trivial, since D is a Stein manifold. We exhibit explicitly a holomorphic trivialization of E -