An extension of the Kramers-Kronig method for treatment of polarized infrared reflectance spectra from the face of low-symmetry crystals, where directions of principal dielectric axes depend on frequency, is proposed. It is shown, how to obtain the frequency dependencies of the complex reflectivity tensor components, using three reflectance spectra measured for different directions of linear polarization of the incident wave, when reflected wave is immediately sent to the detector. The problem is formulated in a form of the system of integral equations, and effective numerical technique is found for solving it. The question of the further recovery of the complex dielectric tensor on the base of the reflectivity tensor, is discussed. The case of the monoclinic crystals is considered in details. An example of the application of the extended Kramers-Kronig method to the reflectance spectra from the (ac)-face of the single-crystal bismuth oxide with the monoclinic lattice is given.