Stability of homogeneous principal bundles with a classical group as the structure group

Let G be a connected semisimple linear algebraic group defined over an algebraically closed field k and P subset of G a parabolic subgroup without any simple factor. Let H be a connected reductive linear algebraic group defined over the field k such that all the simple quotients of H are of classical type. Take any homomorphism rho: P -> H such that the image of rho is not contained in any proper parabolic subgroup of H. Consider the corresponding principal H-bundle E-P(H) = (G x H)/P over G/P. We prove that E-P(H) is strongly stable with respect to any polarization on G/P.