Astronomical spectroscopy at submillimeter wavelengths holds much promise for fields as diverse as the study of planetary atmospheres, molecular clouds and extragalactic sources. Fourier transform spectrometers (FTS) represent an important class of spectrometers well suited to observations that require broad spectral coverage at intermediate spectral resolution. In this paper we present the design and performance of a novel FTS, which has been developed for use at the James Clerk Maxwell Telescope (JCMT). The design uses two broadband intensity beamsplitters in a Mach-Zehnder configuration, which provide access to all four interferometer ports while maintaining a high and uniform efficiency over a broad spectral range. Since the interferometer processes both polarizations it is twice as efficient as the Martin-Puplett interferometer (MPI). As with the MPI, the spatial separation of the two input ports allows a reference blackbody to be viewed at all times in one port, while continually viewing the astronomical source in the other. Furthermore, by minimizing the size of the optical beam at the beamsplitter, the design is well suited to imaging Fourier transform spectroscopy (IFTS) as evidenced by its selection for the SPIRE instrument on Herschel.