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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 thecurves $aP+bQ=0$, $(a:b)\in \mathbb{P}^1$, are irreducible rational curves. Theobtained result shows that such polynomial maps $F$ is invertible if $(0,0)$ isa regular value of $F$ or if the Jacobian condition holds.

Pencil of irreducible rational curves and Plane Jacobian conjecture