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A new hybrid finite element method-boundary element method (FEM-BEM) scheme is proposed for the solution of the nonlinear 2-D Laplace problem. The novelty is an original approach of the BEM where the domain integrals are eliminated at the discrete level by using the FEM approximation of the fundamental solution at every node of the related mesh in the linear regions. The implementation of this FEM-Green approach requires less computational burden than the standard BEM. The coupling with FEM is straightforward and appears to be more natural. The validity of the method is examined through numerical examples.