The well-known Hartman-Grobman Theorem says that a C1 hyperbolic diffeomorphism F can be locally linearized by a homeomorphism Φ.For parameterized systems Fθ,known results show that the corresponding homeomorphisms Φθ exist uniquely in a functional space equipped with the supremum norm and depend continuously on the parameter θ.In this paper,we further extend the results to H?lder dependence of Φθ on 0 by Pugh\'s strategy,but introducing a kind of special H?lder norm instead of the usual supremum norm in the proof to control the linear parts of Fθ.This requires a new H?lder linearization result for every Fθ.