Realistic flight vehicles for reentry into the Earth’s atmosphere are commonly similar to blunted cones. The main reason for blunting a cone is to mitigate high heat loads at the nose. Another reason for blunting the cone is to delay boundary-layer transition. It is commonly understood that the second mode is damped in flow over a cone as the nose radius is increased. This is thought to lead to the delay in transition. Here, a blunted cone at a realistic reentry trajectory point with significant real-gas effects is studied. It is shown, using linear stability theory and direct numerical simulation, that there exist multiple unstable modal instabilities in the boundary layer. One of these modal instabilities is called the supersonic mode, as its phase velocity is supersonic relative to the flow velocity at the edge of the boundary layer. Its growth rate is found to increase with increasing nose radius until a certain nose radius is reached. After this radius, any further increase in nose radius decreases its growth rate. There is adequate agreement between theory and direct numerical simulation for the growth rate, phase velocity and eigenfunction of the supersonic mode. At the reentry conditions tested, the supersonic mode is more likely the cause of boundary-layer transition than the second mode for blunted cones with a small wall-temperature ratio. Initial parametric studies confirm that a decrease in wall temperature amplifies the supersonic mode. Also, the supersonic mode’s growth rate is shown to be a maximum when its phase velocity is aligned with the flow velocity.