This paper presents a simple and effective method to extract the identification quantity of transient pulse waveform produced by the overhead transmission line short-circuit fault. This method employs the second-order time harmonic equation of the power frequency component to convert the fault full-wave data. After the conversion, only the identification quantity remains. This method can amplify high-frequency spectral content by the times of the square of the angular frequency, and hence improve the sensitivity of identifying fault transient. Using the identification quantity, one can clearly observe the arrival time and relative intensity of fault transient. A three-phase half wavelength transmission line of 50Hz/3000km is simulated with PSCAD to illuminate the effectiveness of this method. The effects of fault type, soil resistivity, fault resistance, power frequency fluctuation, sampling rate, transposition length,fault inception angle and white noise are analyzed. Calculated results show that this method can distinguish different fault type and can work effectively at low sampling rate down to 10kHz. This method is helpful for improving the performance of the traveling-wave based fault location method.