The submillimetre-wave spectrum of the SiN radical has been investigated in the laboratory using a source-modulation microwave spectrometer equipped with a negative glow discharge cell. SiN was produced in a SiCl_4_/N_2_ discharge plasma. Twenty-one new fine and hyperfine components up to N=17-16 were observed reaching a frequency as high as 740GHz. The new laboratory measurements provide much improved rest frequencies in the submillimetre spectral region useful for the identification of SiN lines in hot core sources and circumstellar shells.