In 2001, Donaldson proved that the existence of cscK metrics on a
polarized manifold (X,L) with discrete automorphism group implies the
existence of balanced metrics on L^k for k large enough. We show that the
similar statement holds if one twists the line bundle L with a simple
stable vector bundle E. More precisely we show that if E is a simple
stable bundle over a polarized manifold (X,L), (X,L) admits cscK metric
and have discrete automorphism group, then (PE^*, \O(d) \otimes L^k)
admits a balanced metric for k large enough.