The Far-Infrared Surveyor (FIS) onboard the AKARI satellite has a spectroscopic capability provided by a Fourier transform spectrometer (FIS-FTS). FIS-FTS is the first space-borne imaging FTS dedicated to far-infrared astronomical observations. We describe the calibration process of the FIS-FTS and discuss its accuracy and reliability. The calibration is based on the observational data of bright astronomical sources as well as two instrumental sources. We have compared the FIS-FTS spectra with the spectra obtained from the Long Wavelength Spectrometer (LWS) of the Infrared Space Observatory (ISO) having a similar spectral coverage. The present calibration method accurately reproduces the spectra of several solar system objects having a reliable spectral model. Under this condition the relative uncertainty of the calibration of the continuum is estimated to be $pm$ 15% for SW, $pm$ 10% for 70-85 cm^(-1) of LW, and $pm$ 20% for 60-70 cm^(-1) of LW; and the absolute uncertainty is estimated to be +35/-55% for SW, +35/-55% for 70-85 cm^(-1) of LW, and +40/-60% for 60-70 cm^(-1) of LW. These values are confirmed by comparison with theoretical models and previous observations by the ISO/LWS.
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