Abstract: To improve the CCA1 method in reference（Gordon D.Corner cutting and augmentation: An area-preserving method for smoothing polygons and polylinesJ.Computer Aided Geometric Design,2010,27（7）: 551-562）,a new curve subdivision method with area-preserving called CCA（k） method is presented in this paper.This method cuts corners according to the ratio of the adjacent edges while the cutting triangles are isosceles in the CCA1 method,so the limit curve can fit the initial polygon better.The recursive formulas and the well-posed solution of the cutting ratio are obtained in the paper.Meanwhile,the convergence and the continuity of limit curve are proved.For many different kinds of closed polygons,numerical examples show that the good subdivision results can be got by CCA（k） method.