  The second hyperpolarizability $\gamma_N(-3\omega\omega,\omega,\omega)$ of
$N$ double-bond finite chain of trans-polyactylene is analyzed using the
Su-Schrieffer-Heeger model to explain qualitative features of the
size-dependence behavior of $\gamma_N$. Our study shows that $\gamma_N/N$ is
{\it nonmonotonic} with $N$ and that the nonmonotonicity is caused by the
dominant contribution of the intraband transition to $\gamma_N$ in polyenes.
Several important physical effects are discussed to reduce quantitative
discrepancies between experimental and our results
