  We investigate extremal charged black hole solutions in the four-dimensional
string frame Gauss-Bonnet gravity with the Maxwell field and the dilaton.
Without curvature corrections, the extremal electrically charged dilatonic
black holes have singular horizon and zero Bekenstein entropy. When the
Gauss-Bonnet term is switched on, the horizon radius expands to a finite value
provided curvature corrections are strong enough. Below a certain threshold
value of the Gauss-Bonnet coupling the extremal black hole solutions cease to
exist. Since decreasing Gauss-Bonnet coupling corresponds to decreasing string
coupling $g_s$, the situation can tentatively be interpreted as classical
indication on the black hole -- string transition. Previously the extremal
dilaton black holes were studied in the Einstein-frame version of the
Gauss-Bonnet gravity. Here we work in the string frame version of this theory
with the S-duality symmetric dilaton function as required by the heterotic
string theory.
