  The bivariate difference filed $(\mathbb{F}(\alpha, \beta), \sigma)$ provides
an algebraic framework for a sequence satisfying a recurrence of order two and
it could transform the summation involving a sequence satisfying a recurrence
of order two into the first order difference equations in the bivariate
difference field. Based on it, we present an algorithm for finding all the
polynomial solutions of such equations in the bivariate difference field, and
show an upper bound on the degree for polynomial solutions which is sufficient
to compute polynomial solution by using the undetermined method.
