Abstract: With continuous expansion of flight speed and altitude domains, the high-temperature gas effects, especially the thermochemical non-equilibrium (TCNE) effects in hypersonic high-enthalpy boundary layers invalidated the calorically perfect gas (CPG) assumption. They can also largely influence the flow transition process. In recent years, the emergence of unstable supersonic modes in the downstream region of the second mode has been conerned. The so-called supersonic mode refers to the mode with a relative Mach number greater than one at the boundary layer edge, that is, a sound wave that propagates faster than that in the far field. Linear parabolized stability equations (PSE) theory was used to study the critical wall temperature of the supersonic mode under the condition of sharp wedge winding with Mach number 20 and half top angle of 6°. It is found that the lower the wall temperature, the more prone to unstable supersonic mode appeared. Furthermore, the supersonic mode situation and disturbance development form under different Mach number conditions in the flow of the plate boundary layer were explored. It is found that the Mach number continues to increase, the earlier the se-cond mode appears, the maximum growth rate of the second mode decreases, and the peak value of N decreases. At a speci-fic altitude of 30 km, when the Mach number exceeds a certain critical value, the disturbance growth rate and the development form of the supersonic mode are significantly different.