Developing a stable and efficient numerical method for solving the convective diffusion problems continues to be an active and challenging research area because of its importance in prediction of heat and mass transfer and fluid flow. Tests of the diverse methods of this area in the literature reveal that two types of problems appear quite frequently at high P~clet numbers: (1) Parasitic oscillation and/or artificial numerical attenuation ; (ii) Negative values of concentrations or excess temperature. The author's paper [I] presented a hybrid method of fractional steps with L ~stability to overcome these difficulties. But it requires At