A numerical solution to the finite difference of 2D depth-averaged equations on nonstaggered grid points is proposed in this paper. Following locally one-dimensional procedure, the basic equations are split into a pair of one-dimensional equations. Therefore, the solution of a two-dimensional problem is reduced to the solution of a sequence of two one-dimensional problems. The discretization of the split one-dimensional equations is obtained with the use of the original Preissmann operator. Using Fourier's classic linear analysis, stability, dissipation and dispersion with frictional resistance are investigated for the variations of the Courant number and weighting time factor.