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In paper [4] (J. Comput. Appl. Math., 76 (1996), 137-146), a difference scheme for a class of nonlocal parabolic equations with natural boundary conditions was derived by the method of reduction of order and the unique solvability and second order convergence in La-norm are proved. In this paper, we prove that the scheme is second order convergent in L∞ norm and then obtain fourth order accuracy approximation in L∞ norm by extrapolation method. At last, one numerical example is presented.