We propose a new method of solution of the unsteady non-linear Eddington-Vogt-Sweet circulation. We do not use eddy viscosity, in contrast to Tassoul and Tassoul (1982a), and we take the turbulent flow in the radiative region of a rotating main sequence star as an unsteady laminar flow. Analogous to the situation in ordinary gasdynamics (Kawamura and Kuwahara, 1984), results based on our laminar type model of a turbulent flow in a rotating star will complement a series of results by Tassoul and Tassoul for the inner rotation of a star. By employing our method, the following results are obtained. (1) We derive a non-linear partial differential equation of the perturbation as the basic equation of the main bulk of flow in the radiative region. (2) We show that the boundary layer at the interface between the convective and the radiative regions is of the Ekman type. We show ways to resolve the singularity of the meridional velcoity on the interface and give boundary conditions for the main bulk of the flow. (3) We demonstrate that we can construct a non-singular solution which has sufficient degrees of freedom and satisfies the surface boundary conditions of an early type rotating star. We do not need, therefore, a Mestel-Tassoul and Tassoul type surface boundary layer in our treatment. (4) We examine a simple one-dimensional model of our basic equation from the viewpoint of numerical gasdynamics and discuss the astrophysical meaning of the results.