  We explicitly compute the entropy of an extremal dyonic black hole in
heterotic string theory compactified on T^6 or K3\times T^2 by taking into
account all the tree level four derivative corrections to the low energy
effective action. For supersymmetric black holes the result agrees with the
answer obtained earlier 1) by including only the Gauss-Bonnet corrections to
the effective action 2) by including all terms related to the curvature squared
terms via space-time supersymmetry transformation, and 3) by using general
arguments based on the assumption of AdS_3 near horizon geometry and space-time
supersymmetry. For non-supersymmetric extremal black holes the result agrees
with the one based on the assumption of AdS_3 near horizon geometry and
space-time supersymmetry of the underlying theory.
