In a recent publication, a reverse nonequilibrium molecular dynamics (RNEMD) method was presented for computing the mutual diffusion coefficient of liquid mixtures. A concentration gradient and a subsequent mass flux are induced in the system by suitably exchanging molecules in different regions. The algorithm has been successfully tested on Lennard-Jones mixtures and molecular fluid mixtures with molecules having the same number of particles. In this work, a modification is made to the RNEMD method to determine the mutual diffusion coefficient of binary liquid mixtures with molecules having different sizes and masses. To migrate molecules of a different type, the splitting method has been used in this work. Investigation of the resulting steady-state mass fraction profile allows the evaluation of the mutual diffusion coefficient. For validation, the mutual diffusion coefficients of ethane-propane and ethane-pentane liquid mixtures at different compositions and temperatures have been obtained using this method. The mutual diffusion coefficients obtained from the RNEMD simulations are within the error bars of values obtained by equilibrium molecular dynamics for the identical model and conditions. The excess energy released due to the exchange of molecules is efficiently removed by strongly coupling a local thermostat in the region around the insertion point. There is no heating of the analysis region.