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Exact error linearisation is a well-established nonlinear observer design method which is difficult to apply as it requires the solution of a system of partial differential equations. To avoid this difficulty, two observers and sufficient conditions for their global convergence are proposed. The methods combine the high-gain and exact error linearisation approaches. Assuming both the observer canonical form exists and the system's output injection is globally Lipschitz, both observer gain vectors can be computed efficiently without knowledge of either the observer canonical form or the associated transformation. The proposed observers are particularly well suited to systems which are globally Lipschitz in observer canonical form but not in the observable coordinates. This last requirement is sufficient for a traditional high-gain design. An example is provided which demonstrates the methods.