  Dual Bernstein polynomials of one or two variables have proved to be very
useful in obtaining B\'{e}zier form of the $L^2$-solution of the problem of
best polynomial approximation of B\'{e}zier curve or surface. In this
connection, the B\'{e}zier coefficients of dual Bernstein polynomials are to be
evaluated at a reasonable cost. In this paper, a set of recurrence relations
satisfied by the B\'{e}zier coefficients of dual bivariate Bernstein
polynomials is derived and an efficient algorithm for evaluation of these
coefficients is proposed. Applications of this result to some approximation
problems of Computer Aided Geometric Design (CAGD) are discussed.
