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Stability and dispersion analysis of higher-order three-step locally one-dimensional (LOD) finite-difference time-domain (FDTD) method is presented here. This method uses higher order cell-centred finite-difference approximation for the spatial differential operator and second-order finite difference approximation for the time differential operator. Unconditional stability of the higher-order three-step LOD-FDTD method is analytically proven and numerically verified. Numerical results show improvement in the overall performance of higher-order three-step LOD-FDTD method compared with that of second order. Also, the effects of the order of approximation, the time step and the mesh size on numerical dispersion are explained through analytical results and verified by simulation results.