We report on the far–infrared optical properties of melamine characterized by terahertz time–domain spectroscopy (THz–TDS). Transmission measurement reveals three low–frequency vibration modes at 1.99, 2.25, and 2.61 THz, which may provide fingerprints for direct melamine detection. By combining THz–TDS with Fourier transform infrared (FTIR) spectroscopy, an overall low–frequency optical response of melamine is presented in an extended spectral range of 0.2–6.2 THz. In this range, the low-frequency vibration mode at 3.96 THz is recorded via FTIR. The measured THz spectra are well fit by the multiple–oscillator model, thereby demonstrating that the low–frequency THz response of melamine is a consequence of the lowest four vibration modes.