Abstract: Nonlinear approximation has been widely applied to many fields. As a kind of simple and effective approach, the hinge-finding algorithm has particular advantage. The algorithm uses the hinging hyperplanes model that uses hinging hyperplanes as basis functions in expansion. By means of theoretically analyzing it is shown that the representation capability of the model is deficient. The deficiency causes the model's inability to achieve optimal approximation. In this paper the hinging hyperplanes model is extended and the deficiency is remedied at a two-dimensional space. The extended model has enough representation capability, which theoretically ensures the possibility to achieve optimal approximation. In simulation, with the same number of parameters, the new algorithm gets better approximation precision and less prediction error than those of the hinge-finding algorithm.