  We use the entropy function formalism to study the effect of the Gauss-Bonnet
term on the entropy of spherically symmetric extremal black holes in heterotic
string theory in four dimensions. Surprisingly the resulting entropy and the
near horizon metric, gauge field strengths and the axion-dilaton field are
identical to those obtained by Cardoso et. al. for a supersymmetric version of
the theory that contains Weyl tensor squared term instead of the Gauss-Bonnet
term. We also study the effect of holomorphic anomaly on the entropy using our
formalism. Again the resulting attractor equations for the axion-dilaton field
and the black hole entropy agree with the corresponding equations for the
supersymmetric version of the theory. These results suggest that there might be
a simpler description of supergravity with curvature squared terms in which we
supersymmetrize the Gauss-Bonnet term instead of the Weyl tensor squared term.
