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This paper presents a new technique to find the complex permittivity of low-loss dielectric materials in microwave band of frequencies. The technique, in its general form, involves completely filling with the dielectric material a thick rectangular window in a rectangular waveguide and measuring the transmission scattering parameter, S21, of the waveguide with a vector network analyzer. Theoretically, S21 is determined for the same window by solving magnetic field integral equations (MFIEs), which are setup with the help of a rectangular cavity and a semi-infinite waveguide Green's functions. The MFIEs are solved using method of moments (MoM). Newton-Raphson method is, then, used to match the theoretical S21 with the measured one to estimate the unknown complex permittivity of the low-loss dielectric material. Four experiments are performed, three over X-band and one over S-band of frequencies with three dielectric materials - Teflon, Plexiglas and C-STOCK AK. For two cases over X-band, the results obtained are compared with those obtained from the Hewlett-Packard method to validate our technique.