The object of the present paper is to study a special type of spacetime. It is proved that in a conformally flat $(WRS)$_{4}$ spacetime with non-zero scalar curvature the vector field $\rho$ defined by $ɡ(X,\rho) = E(X)$ is irrotational and the integral curves of the vector field $\rho$ are geodesics. We also show that a conformally flat $(WRS)_{4}$ spacetime with non-zero scalar curvature is the Robertson-Walker spacetime. Next possible local cosmological structure of such a spacetime is determined. Finally, we construct an example of a conformally flat $(WRS)_{4}$ space-time with non-zero scalar curvature.