Abstract: At free-stream Mach number larger than 4, the second mode is the dominant instability mode in supersonic boundary layers. According to the findings from receptivity research, one important way to generate the second mode is through intermodal exchange, by which the excited fast mode in the boundary layer synchronizes with the second mode when travels downstream. In this paper, the intermodal exchange between the fast mode and the second mode in a supersonic boundary layer is investigated numerically. Two coefficients, i.e. the amplitude and region of intermodal exchange are defined. Their relations are established with respect to the disturbance frequency. Based on linear stability theory, a new method accounting for the intermodal exchange is developed to compute the evolutions of the disturbances. The parabolized stability equations is used to verify the new method. It is shown that, under a wide range of wall temperature conditions, the newly developed method can accurately predict the evolutions of the disturbance considering the process of intermodal exchange between fast mode and the second mode. With considerations of the initial amplitude of the excited fast mode and a transition criterion, this method can be easily used to predict transition of a boundary layer. Since it considers the generation of the second mode through intermodal exchange, it accounts for more physics than the conventional transition prediction method.