Most recently, various programs of the Acoustic Thermometry of the Ocean have been planned or are under way in the worldwide. However, it is difficult to analyze precisely the sound propagation in the shallow water with sloping bottom, because the abrupt variations of the density and sound speed occur at interfaces in the water-sediment. The conventional finite difference scheme based on Crank-Nicolson method for solving sound wave propagation in the wedge model has a truncation error of second-order in the depth direction. In the environments having abrupt changes in density and sound speed, a more accurate treatment for PE method is required to obtain underwater sound propagation. To reduce the truncation error for the finite-difference, we apply the Douglas operator scheme having a truncation error of fourth-order. The resulting matrix equation is tridagonal for z-discretization and is easy to solve numerically using a simple Thomas's algorithm. In order to show the usefulness of the present method, numerical results are presented for the shallow water model considering large changes in velocity and density at the water-bottom interface and are also compared with existing other methods.