Abstract: Based on Bernstein class functions and Bézier class curves, the representation and some properties of Bernstein Bézier class curves and Bernstein Bézier class curves with weighted factors are studied Further research on the relation between Bernstein Bézier class curves with weighted factors and Bézier curves indicates that Bernstein Bézier class curves are the extended forms of Bézier curves At the same time, the theory of Bernstein Bézier class curves can be devoted to a systematical reparametrization method of Bézier curves The method in this sense is discussed in details It is concluded that this method has many advantages in some ways So far, it’s the universal one of the reparametrization method of Bézier curves Compared with other methods, this algorithm is very simple