  We consider the perturbation of tachyon about the extremal ground state of a
two-dimensional (2D) electrically charged black hole. It is found that the
presenting potential to on-coming tachyonic wave takes a double-humped barrier
well. This allows an exponentially growing mode with respect to time. This
extremal ground state is classically unstable. We conclude that the 2D extremal
electrically charged black hole cannot be a candidate for the stable endpoint
of the Hawking evaporation.
