An expression for the binary collision contribution to the first order memory function of the transverse current correlation function has been obtained using the cluster expansion technique for particles of a fluid interacting via a continuous potential. The resulting expression involves the static pair correlation function and the time dependence of position, momentum, and acceleration of a particle. In the long wavelength limit our expression determines the time development of the autocorrelation function of transverse stress.:These time-dependent functions have been evaluated numerically for the Lennard-Jones potential for some thermodynamic states and results have been compared with molecular dynamics data. It has also been found that for a hard sphere interaction our expression for the shear viscosity reduces to the Enskog result.