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Numerical procedures for solving the time-domain Maxwell equations based on the theory of characteristics were successfully developed. Both explicit and implicit methods were formulated by the time-central and spatial-windward algorithm to better describe wave motion. A new trapezoidal consistent implicit scheme was shown to be unconditionally stable for the linear initial value system and was able to generate numerical solutions comparable to those of the established explicit method. The formulation of the three-dimensional system including generalized coordinate system was completed but not explored. The present 2-D results on Cartesian frame demonstrated a potential for numerical efficiency improvement. Time-domain Maxwell equation, Trapezoidal consistent implicit scheme, Cartesian frame.