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An algorithm for reconstructing the characteristics (charge, mass, and energy) of cosmic-radiation nuclei with 20- to 200-MeV/nucleon energies is described. The detector is a telescope of three two-coordinate planes with two 1-mm-thick iron filters inserted between them. Each plane is composed of two strip silicon detectors with 3.6-mm-wide orthogonally oriented strips, an effective area of 6 × 6 cm2, and a thickness of 380 μm. The algorithm for reconstructing the nuclei characteristics is based on the analysis of how the specific ionization losses change as the nuclei pass through the filter material. The results of the Monte Carlo simulation are presented for the energy dependence of the telescope acceptance and the energy deposited in the detectors by different nuclei in view of the detector calibration on the nuclear beams of the accelerator. The mass resolution of the telescope is ∼30, 12, and 5% for He, N, and Al nuclei, respectively. The energy resolution, which is ∼20%, is much the same for all nuclei.