Following the discovery by Kao and Hockman(1-3) that ultra-low-loss optical fibres could be made from pure silica through the elimination of impurities, the ability to guide signals effectively at optical wavelengths has been assured. But there remains an important region of the spectrum-from 30 to 3,000 GHz (the millimetre-submillimetre band)-where low-loss waveguides are unknown. The main problem here in finding low-loss solids is no longer one of eliminating impurities, but is due to the presence of intrinsic vibration absorption bands(4-6). And the use of highly conducting materials is also precluded owing to high skin-depth losses(7,8) in this part of the spectrum. Here we show that a combination of material and waveguide geometry can circumvent these difficulties. We adopt a ribbon-like structure with an aspect ratio of 10:1, fabricated from ceramic alumina (Coors＇ 998 Alumina), and the resulting waveguide has an attenuation factor of less than 10 dB km(-1) in the millimetre-submillimetre band. This attenuation is more than 100 times smaller than that of a typical ceramic (or other dielectric) circular rod waveguide and is sufficient for immediate application.