  We determine the corrections to the entropy of extremal black holes arising
from terms quadratic in the Riemann tensor in $N=2, D=4$ supergravity theories.
We follow Wald's proposal to modify the Bekenstein-Hawking area law. The new
entropy formula, whose value only depends on the electric/magnetic charges, is
expressed in terms of a single holomorphic function and is consistent with
electric-magnetic duality. For string effective field theories arising from
Calabi-Yau compactifications, our result for the entropy of a certain class of
extremal black-hole solutions fully agrees with the counting of microstates
performed some time ago by Maldacena, Strominger, Witten and by Vafa.
