Abstract: The wave equation of electric in the waveguide can be translated into a coupled difference equation of second order by centered difFerency approximation. This coupled difference equation can be reduced to a very compact decoupled difference equation which contains only one electric component, the Ey, when the discontinuity under investigating only relates to the x-direction in the rectangular waveguide. This difference eqiiation can be computed simply and the memory of computer as well as the CPU time are saved greatly comparing with the conventional FDTD algorithm. The condition of its stability, the dividing of the spatial grid and the absorbing condition of the algorithm are given and compared with the conventional FDTD method. Both data examples computed by the new algorithm and published ones are presented,which show a good agreement.