A stationary double-mirror Fourier transform spectrometer is applied to measure optical transmittances over the wavelength range 400-100 nm. The set-up uses a two-beam wavefront-splitting interferometer having no moving parts and no wavelength-sensitive beamsplitter. The spectral response of the spectrometer with the charge-coupled detector is determined over the wavelength range. Preliminary estimates of the linearity and repeatability of the spectrometer performance are given. In measurements of the transmittances of neutral density filters, the standard deviation was about 3*10-3. In measurements of the interference filter transmittances, the relative uncertainty of the line position was a few parts in 10-4. As a relatively low-resolution, but mechanically stable, compact and inexpensive instrument, the double-mirror spectrometer is ideal for measuring properties of wideband radiation sources in use in the field.