For the numerical simulation of transport problems with high cell Peclet number, the coefficient matrix of finite difference equations may lose the diagonal dominance if a scheme more accurate than the first-order upwind is used to approximate the convection terms. Hence, in many cases it is difficult to choose a suitable relaxation factor a priori for these schemes when the commonly used iterative method is applied to obtain the convergent solution. However, it is found that after appropriate normalization, an easier determined relaxation factor useful to all three schemes studied here, i.e., second-order central differencing, second-order upwinding, and QUICK, exists. Two model problems are used to compare the performances among the three schemes. The second-order central differencing is found to be less efficient in the cases investigated. Without the aid of the normalization, the second-order upwind scheme has the widest range of allowable values for the relaxation factor. Yet QUICK may be computationally more efficient after normalization. This is mainly because the number of iterations needed for QUICK is less sensitive to the choice of the relaxation factor when the optimum value isn't known. For a flow problem with non-constant velocities, the present method becomes the iterative algorithm with different relaxation parameters for different points, i.e., a local relaxation method. It is demonstrated that, in addition to helping choose the relaxation factors, this idea may also substantially reduce the computing time compared with the iterative algorithm with the uniform relaxation factor for all the grid points.