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A new method has been proposed for implementing the essential boundary condition and the natural one to the Element-Free Galerkin Method (EFGM). Furthermore, the performance of the proposed method has been investigated for a nonlinear Poisson problem. The results of computations show that the accuracy degradation of the numerical solution can be suppressed by using the proposed method. In addition, the convergence performance of the proposed method is more stable than that of the standard EFGM. Therefore, it might be concluded that the proposed method is useful for solving the nonlinear Poisson problem.