The basic ideas of the general boundary element method (BEM) proposed by Liao (The quite general BEM for strongly nonlinear problems, in: C. A. Brebbia, S. Kim, T. A. Osswald, H. Power (Eds.), Boundary Elements XVII, Computational Mechanics Publications, Southampton, 1995, pp. 67–74. International Journal of Numerical Methods for Fluids, 1996, 23, 739–751. International Journal of Numerical Methods in Fluids, 1997, 24, 863–873) and Liao and Chwang ( International Journal of Numerical Methods for Fluids, 1996, 23, 467–483) are further greatly generalized by introducing two nonzero parameters to construct homotopies. This general BEM is valid for strongly nonlinear problems, including even those whose governing equations and boundary conditions do not contain any linear terms. Therefore, it can greatly enlarge the application areas of the boundary element method as a numerical methodology. A two-dimensional nonlinear differential equation is used to verify the validity of the further generalized boundary element method. Moreover, this example illustrates that, by means of the proposed general boundary element method, iteration is not absolutely necessary for nonlinear problems. This shakes the absolutely governing place of iterative methodology of the boundary element method for nonlinear problems, and might be beneficial for us to understand the essence of solving nonlinear problems.