  Let $S$ be a rational projective surface given by means of a projective
rational parametrization whose base locus satisfies a mild assumption. In this
paper we present an algorithm that provides three rational maps
$f,g,h:\mathbb{A}^2 --\to S\subset \mathbb{P}^n$ such that the union of the
three images covers $S$. As a consequence, we present a second algorithm that
generates two rational maps $f,\tilde{g}:\mathbb{A}^2 --\to S$, such that the
union of their images covers the affine surface $S\cap \mathbb{A}^n$. In the
affine case, the number of rational maps involved in the cover is in general
optimal.
