The fundamental TE10 mode in a rectangular waveguide of a square cross section is degenerate with TE01 mode. A quarter wavelength resonator made of a dielectric square waveguide is, therefore, applied for a small-sized bandpass filter, just like dual mode filters for base stations in the mobile communication. In this paper, the methods to couple the two modes are first studied, including cutting a corner of the resonator and adding some metal electrodes on its end face. Both methods help to flow the rf current of the odd mode at the corner, resulting in decrease of the series inductance and thus increase of the resonant frequency. The coupling constant, that is proportional to the difference of the odd and even-mode's resonant frequency, can be controlled by the perturbations mentioned above. The coupling to the external circuit is adjusted by an electrode fabricated also on the end face. It is connected to a microstrip line and capacitively couples to the resonant modes. The coupling strength increases with the dimension of the electrode. The adjustment of the resonant frequency is carried out by the similar electrode on the end face and connected to the center of the side of the square cross section. The frequency decreases with the length of the electrode. The unloaded Q is measured to be of around 500 for 5510 mm resonator of εr=93. The optimum aspect ratio for the resonator is found in terms of the Q value. The simplest bandpass filter, i.e., a two-stage bandpass filter is designed and fabricated using 5510 mm resonator. It is mounted in a square hole made in a printed circuit board and excited by a microstrip line. The frequency characteristics are in good agreement with the expected values.