Abstract: A new algorithm to reduce a cubic Bézier curve to piecewise quadratic Bézier curves based on choosing appropriate subdivision points is presented.The computation of the error bounds is also discussed.Inflection point and then points of maximum curvature are preferably chosen as the subdivision points.Experiments show that our method can result in less number of quadratic Bézier curve segments compared with other methods in addition to the advantages of end point interpolation and GC¹ continuity.