An exact analysis of the natural convection in unsteady Couette flow of a viscous incompressible fluid confined between two vertical parallel plates in the presence of thermal radiation is performed. The flow is induced by means of Couette motion and free convection currents occurring as a result of application of constant heat flux on the wall with a uniform vertical motion in its own plane while constant temperature on the stationary wall. The fluid considered here is a gray, absorbing-emitting but non-scattering medium, and the Rosseland approximation is used to describe the radiative heat flux in the analysis. The dimensionless governing partial differential equations are solved using Laplace transform technique. Numerical results for the velocity, the temperature, the skin-friction, the Nusselt number, the volume flow rate and the vertical heat flux are shown graphically. The effect of different parameters like thermal radiation parameter, Grashof number, Prandtl number and time are discussed. It is observed that the momentum and thermal boundary layer thickness decreases owing to an increase in the value of the radiation parameter. An increase in the Grashof number is found to increase the velocity of air and water and to decrease the skin-friction at the moving plate.