The main objective of this paper is to propose a framework for the design of local asymptotic observers, with arbitrarily fast rate of convergence, for autonomous nonlinear systems that are not in observability canonical form. The proposed methodology does not require the knowledge of the inverse of the observability map. Such a goal is pursued by coupling a high-gain observer with a system that is able to locally dynamically invert the observability map. (C) 2019 Elsevier Ltd. All rights reserved.