  We discuss the two-dimensional (2D), $\epsilon<2$ extremal ground states of
charged black hole. Here $\epsilon$ is the dilaton coupling parameter for the
Maxwell term. The complete analysis of stability is carried out for all these
extremal black holes. It is found that they are all unstable. To understand
this instability, we study the non-extremal charged black hole with two (inner
and outer) horizons. The extremal black holes appear when two horizons
coalesce. It conjectures that the instability originates from the inner
horizon.
