A part of the authors have been proposed a few nonlinear normalization methods using line density for handwritten characters and it was verified that those nonlinear methods were more effective than a linear method. Those nonlinear methods, however, could not use two-dimensional information of the line density, because the line density was projected on to the axes of coordinates. This paper proposes an extended nonlinear normalization method which uses two-dimensional information of the line density. It is confirmed that the proposed method is more powerful than conventional methods by experiments tested on the handwritten character database ETL-8.