In this paper, a new explicit transformation method between Bezier and polynomial representation is proposed. An expression is given to approximate (n + 1) Bezier control points by another of (m + 1), and to perform simple and sufficiently good approximation without any additional transformation, such as Chebyshev polynomial. A criterion of reduction is then deduced in order to know if the given number of control points of a Bezier curve is reducible without error on the curve or not. Also an error estimation is given only in terms of control points. This method, unlike previous works, is more transparent because it is given in form of explicit expressions. Finally, we discuss some applications of this method to curve-fitting, order decreasing and increasing number of control points.