The problem of accuracte imposition of essential boundary conditions in the element free Galerkin method is discussed. Using this method some difficulties often occur, because the moving least squares interpolants used in this method lack the delta function property of the usual finite element or boundary element method shape functions. A simple and logical strategy to avoid the above problem is proposed. In this method a discrete norm is typically minimized in order to obtain certain variable coefficients. The strategy is proposed to involve the new definition of this discrete norm. It is shown that the proposed strategy works satisfactory in all numerical examples for the 2-D potential problems, which are presented in the paper. A discussion of the boundary condition is given and some recommendations regarding strategies for refinements in order to improve the accuracy of the numerical solution of the proposed method is made.