Optical resonator with high Q value can be used as a core component of the resonator optic gyro, with which the miniaturization and integration would be achieved. The coupling system composed of the disk cavity which is made by traditional micro-electro-mechanical system process and the tapered fiber which is drawn by melting method. When the disk cavity is coupled with the fiber at different places of the tapered region, by swapping input and output there is observed the deviation in the output transmission spectrum, also the resonant frequency, coupling efficiency and the Q value are changed, i.e., the non-reciprocity phenomenon appears. Then the distribution characteristics of the tapered fiber evanescent field are simulated with Rsoft software. The reason of the non-reciprocity is analyzed theoretically. According to the statistics of the output data when the disk cavity is coupled with the fiber at different places of the tapered region, it is found that the non-reciprocity can be eliminated effectively when the coupling happens at the center of the fiber tapered region. And this finding can be used to suppress the non-reciprocity noise produced by the coupling system composed of tapered fiber and resonant cavity in the resonator optic gyros application.