  The $\Lambda$ parameter on the anisotropic lattice, the spatial and
temperature coupling constant $g_{\sigma}$, $g_{\tau}$ and their derivative
with respaect to the the anisotropy parameter $\xi$ are studied perturbatively
for the class of improved actions, which cover tree level Symanzik's, Iwasaki's
and QCDTARO's improved actions. The $\eta(=g_{\tau}/g_{\sigma})$ becomes less
than 1 for Iwasaki's and QCDTARO's action, which is confirmed nonperturbatively
by numerical simulations. Derivatives of the coupling constants with respect to
the anisotropy parameter, $\partial g_{\tau}/\partial \xi$ and $\partial
g_{\sigma}/\partial \xi$, change sign for those improved actions.
