  This is a report of our recent investigation on the extremal dilatonic black
holes in four dimensional Gauss-Bonnet gravity. We found that a global solution
can exist only when the dilaton coupling is less than a critical value which
can be determined numerically. Moreover, the black hole horizon is stretched by
the Gauss-Bonnet correction and the entropy is twice the value given by
Bekenstein-Hawking formula.
