  We discussed the full unitary matrix models from the view points of
integrable equations and string equations. Coupling the Toda equations and the
string equations, we derive a special case of the Painlev\'{e} III equation.
From the Virasoro constrains, we can use the radial coordinate. The relation
between $t_{1}$ and $t_{-1}$ is like the complex conjugate. %An implicit to the
$t\bar{t}$ fusion of topological sigma model %is therby expected.
