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A modified precise integration time-domain (PITD) method, called PITD(4) algorithm, is presented in order to mitigate the numerical dispersion errors of a recently proposed PITD method. The PITD(4) method is based on both the fourth-order accurate finite-difference scheme and the precise integration technique. Both the stability condition and the numerical dispersion relations of the PITD(4) method are derived analytically and the effects of spatial and time steps on the numerical dispersion are investigated in detail. It is found that with the precise integration technique, the stability condition of the PITD(4) method is much larger than the Courant-Friedrich-levy (CFL) stability condition of the conventional finite difference time domain; with the fourth-order accurate finite-difference scheme, the numerical dispersion errors of the PITD(4) method are much less than that of the PITD methods. Numerical examples are presented to validate the accuracy and the effectiveness of the PITD(4) method, and to verify our analysis of the numerical dispersion characteristics of the PITD(4) method.