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We prove that the set of fiber-bunched $SL(2,\mathbb{R})$-valued H\"{o}ldercocycles with nonvanishing Lyapunov exponents over a volume preserving,accessible and center-bunched partially hyperbolic diffeomorphism is open.Moreover, we present an example showing that this is no longer true if we donot assume acessibility in the base dynamics.

The set of fiber-bunched cocycles with nonvanishing Lyapunov exponents over a partially hyperbolic map is open