Terahertz (THz) absorption spectra have been applied to measure the compositions of amino acid samples. Because the concentration information about a specific composition is involved in its spectrum, keeping the spectrum length and dynamic range as wide as possible is essential for precise measurements. It is well known that a spectrum is always contaminated by apparatus noises. In this paper, we present a criterion for noise cutting based on wavelet transform, which usually extends the range determined by traditional threshold criterion. Finally, the improvement on measurement precision shows the validity of the new criterion.