  The new mode of instability found by Tunney et al. is studied with viscous
stability theory in this article. When the high-speed boundary layer is subject
to certain values of favorable pressure gradient and wall heating, a new mode
becomes unstable due to the appearance of the streamwise velocity overshoot
($U(y)>U_\infty$) in the base flow. The present study shows that under
practical Reynolds numbers, the new mode can hardly co-exist with conventional
first mode and Mack's second mode. Due to the requirement for additional wall
heating, the new mode may only lead to laminar-turbulent transition under
experimental (artificial) conditions.
