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A novel idea of azimuthal partition to generate high power microwave (HPM) with two frequencies in a single device is put forward for the first time in this paper. According to this idea, a magnetically insulated transmission line oscillator (MILO) that could generate HPM with two stable and separate frequencies is designed. To distinguish this new device from a traditional MILO, it is named bifrequency MILO (BFMILO) in this paper. The high-frequency characteristics of BFMILO are investigated, and it is simulated through 3-D PIC codes. The results of particle simulation are presented: Employing an electron flow of 420 kV and 38 kA, an L-band BFMILO can generate about 1.3 GW of HPM with two frequencies. They are 1.27 and 1.49 GHz, respectively. The power efficiency is about 8.1%. The amplitude difference of the spectrum between the two frequencies is about 0.4 dB. In addition, preliminary experimental results are also presented: When the input voltage is 420 kV and the current is about 34 kA, a BFMILO can generate over 620 MW of HPM. The two frequencies are 1.26 and 1.45 GHz, respectively. The power efficiency is over 4.3%. This paper preliminarily proves the feasibility that BFMILO can generate HPM with two frequencies, and this pointed out a new direction of HPM investigations.