Experimental results indicate that there exist two stable discharge operation points in a self-excited mode Hall effect thruster. During the operation, the discharge operation point jumps to and fro between two values, which greatly influences the physical process of plasma discharge in the thruster channel and the comprehensive performance of thrusters. In this paper, by using the relationship between discharge magneto-ampere characteristic curve and magnetic field coil current curve, we propose the physical mechanism of forming the discharge bistable characteristic. On the basis of the mechanism, a method of stabilizing the single discharge operation point is presented through changing the slope of magnetic field coil current curve. The physical explanation is given through established one-dimensional dynamic fluid model for self-excited mode, and the results are approved by the self-excited experiment.