  We are concerned with the behavior of the polynomial maps $F=(P,Q)$ of
$\mathbb{C}^2$ with finite fibres and satisfying the condition that all of the
curves $aP+bQ=0$, $(a:b)\in \mathbb{P}^1$, are irreducible rational curves. The
obtained result shows that such polynomial maps $F$ is invertible if $(0,0)$ is
a regular value of $F$ or if the Jacobian condition holds.
