The transient field in a moving isotropic medium due to a current source of arbitrary time dependence is formulated and solved with the aid of an independent pseudo-time variable. The approach is similar to D'Alembert's method of solving the one-dimensional scalar wave equation, except that we are dealing with Maxwell's equations with two constitutive relations characterizing a moving medium. This new method appears to be simpler than the one used by Compton [1] who invoked a four-dimensional space-time differential operator and derived several new mathematical formulas covering both the spatial and the time domain simultaneously in order to solve the Maxwell-Minkowski equations. In our treatment, only conventional theorems in spatial domain are needed and the result is also cast in a more recognizable form.