We introduce a new definition of localization for frames which eliminates the dependence on the indexing of the frames. Two main results of Gröchenig are extended to this definition, namely that the dual of a localized frame is also localized, and a frame localized with respect to another frame is a Banach frame for the associated family of Banach spaces. These results parallel the results of a more recent paper by Fornasier and Gröchenig.