  In this paper, a new method to compute a B\'ezier curve of degree n = 2m-1 is
introduced, here formulated as a set of points whose coordinates are calculated
from two Hankel forms in $\C^m$. From Vandermonde factorizations of the two
associated Hankel matrices $H_x$ and $H_y$, the Hankel forms can be easily
calculated, thus yielding points on the B\'ezier curve. Here, a new proof of
the existence of a Vandermonde factorization of regular Hankel matrix is given
from Pascal matrices techniques. But, even when the Hankel matrix associated to
the form is singular, the method can still be used by shifting its
skew-diagonal and counteracting it after, which is pratically done without
costs.. By comparing this new method with a Pascal matrix method and
Casteljau's, we see that the results suggest that this new method is very
effective with regard to accuracy and time of computation for various values of
n.
