  We demonstrate linear stability of the dilatonic Black Holes appearing in a
string-inspired higher-derivative gravity theory with a Gauss- Bonnet
curvature-squared term. The proof is accomplished by mapping the system to a
one-dimensional Schrodinger problem which admits no bound states. This result
is important in that it constitutes a linearly stable example of a black hole
that bypasses the `no-hair conjecture'. However, the dilaton hair is
`secondary'in the sense that it is not accompanied by any new quantum number
for the black hole solution.
