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Classical resonator spectroscopy methods have been realized for the first time in the submillimeter wave range. A resonator spectrometer was developed earlier at the IAP RAS on the basis of an open Fabry-Perot resonator excited by the radiation of a backward wave oscillator whose frequency is stabilized by the phase lock loop system. This spectrometer is successfully used for high-precision measurements of the dielectric properties of solid, liquid, and gaseous dielectrics as well as for the metal and coating reflection measurements in the 36-370 GHz range. In this paper, we report an extension of the upper limit of the spectrometer operation frequency to 520 GHz. Features of operation of the main spectrometer systems in the extended frequency range are analyzed. The broadband measurements of absorption in modern MPCVD diamonds are presented. A continuous record of the absorption spectrum of the laboratory atmosphere in the 350-500 GHz range obtained for the first time by the high-sensitivity microwave method is demonstrated. Further prospects for extension of the spectrometer range to terahertz frequencies are discussed.