The studies of the quantum corrections for the anisotropy parameter,$eta(=xi_R/xi_B)$, for the improved actions, $beta (C_0 L({Plaq.}) + C_1 L({Rect.}))$, are proceeded in the medium to strong coupling region on anisotropic lattices. The global features for the $eta$ parameters as a function of $beta$ and the coefficient $C_{1}$ have been clarified. It has been found by the perturbative analysis that as $C_1$ decreases, the slope of the $eta(beta)$ becomes less steep and for the actions whose $C_{1}$ is less than -0.160, $eta$ decreases as $beta$ decreases, contrary to the case of the standard action. In the medium to strong coupling region, the $eta$ parameter begins to increase as $beta$ decreases for all $C_{1}$. This means that for the actions with $C_{1} < -0.160$, the one-loop perturbative results for $eta$ break down qualitatively and the $eta$ parameters have a dip. As a result of this dip structure the $eta$ for Iwasakis action remains close to unity in the wide range of $beta$.
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