The characteristics of a beta spectrometer that consists of a total-absorption Si(Li) detector and a drift Si detector are presented. Using this spectrometer, it is possible to efficiently separate β radiation of nuclei from concomitant X and γ rays. The method is based on coincidences between signals from the thick and thin detectors. The spectrometer can be used to precisely measure the shape of the β spectra of various radioactive nuclei, in particular, of the ¹⁴⁴Pr nucleus, which is the most promising antineutrino source for searching for neutrino oscillations into a sterile state.