The ultraviolet (UV) instability of silicon photodiodes is a very complex phenomenon. The change in spectral responsivity after UV exposure can depend on the level of irradiance and total radiant exposure, duration of exposure, wavelength of the UV radiation, the type of photodiode, and the way the photodiode was stored and used before UV exposure. For a systematic investigation, the responsivity change must be determined not only at the wavelength of UV exposure but throughout the whole spectral range in which the photodiode is used. Obviously, a fast method is needed to perform corresponding measurements over a wide range of parameters. Therefore a new, fast and accurate technique based on Fourier-transform spectroscopy was used to study the UV stability of silicon photodiodes in detail. Results are presented for different types of silicon photodiodes (Kamamatsu S1337 and S5227 diodes, a novel PtSi-n-Si Schottky photodiode, and UVG and AXUV photodiodes from International Radiation Detectors).