In this study, approximate derivative (AD) signal processing method using synchronous voltages data, based on the traveling wave theory, was developed to determine fault locations in transmission lines. The first aerial mode voltage signals were obtained by applying the Clarke transformation to the voltage signals that occur after a short circuit fault. Then, by taking the first AD of the aerial mode voltage signals, the traveling waves were obtained. Finally, the location of the fault was found by using the time difference information of the traveling waves, wave velocity value and transmission line length. The proposed signal processing method was found to be effective in determining the location of faults. It was tested and compared to the discrete wavelet transform (DWT) for various fault conditions. Based on the simulation results, the proposed method was found to have a slightly higher success rate than DWT, in general. Moreover, it can work with low sampling frequencies, and it provides a better resolution than DWT to display the traveling waves in noise conditions.