Abstract: In his book "Numerical Control Professor P. Bezier gives an excellent exposition of his technique in CAGD. Bezier's Basic functions fn,j （ u ） are shown in （ 2 ） and （ 3 ）. Bezier's curves have a number of important and interesting geometric properties of the basic functions. As there has been no literature on the derivation of these basic functions sofar, this paper attempts to prove in two different ways that the expressions of basic functions can be determined completely by three simple and reasonable geometric properties of the Bezier's curves.