Conventional Fourier-transform mixes the frequency components of the entire temporal terahertz waveform in one frequency domain; therefore, it cannot distinguish the terahertz frequency in the main pulse from the noise frequency in the pulse tail. Thus traditional Fourier-transform produces inconsistent spectra from different scanning lengths of terahertz pulse. And the interference spectrum appears when the THz echo pulse is recorded. The authors applied wavelet-transform and removed the inconsistent spectra and the interference spectra. Wavelet-transform technique exhibited the local frequency of THz in different time locations. This technique would find applications in THz time-resolved spectroscopy.