  In this paper we study the extension of structure group of principal bundles
with a reductive algebraic group as structure group on smooth projective
varieties defined over algebraically closed field of positive characteristic.
Our main result is to show that given a representation {\rho} of a reductive
algebraic group G, there exists an integer t such that any semistable G-bundle
whose first t frobenius pullbacks are semistable induces a semistable vector
bundle on extension of structure group via {\rho}. Moreover we quantify the
number of such frobenius pullbacks required.
