A module equipped with a non-radiative dielectric waveguide in accordance with this invention comprises a pair of parallel flat conductors arranged at a space of 1/2 or below of a high frequency signal wavelength .lambda. and a dielectric strip extending between these parallel flat conductors. This dielectric strip is formed from a cordierite ceramic having a dielectric constant of 4.5 to 8, especially 4.5 to 6. Conversion of an electromagnetic wave of LSM mode to an electromagnetic wave of LSE is minimal. When the module has a dielectric strip having a steep curved portion having a small radius of curvature, the transmission is possible with a low loss, and the band width of a high frequency signal is broad.