Abstract: The problem of reducing the degree of Bézier curve approximately from n to n-1 under the meaning of L2-norm between two curves is studied. During the process, constrained Legendre polynomials are introduced and the explicit form of fit curve is presented. In addition, an explicit error estimate is given and the algorithm of the best subdivision is justified. A fast, stable and good-result algorithm is accomplished. During the font transformation, an integral algorithm is achieved.