  All the linear alpha-prime corrections, however excluding the gravitational
Chern-Simons correction, are studied in the toroidally compactified critical
Heterotic string theory. These corrections are computed to the entropy for a
BPS static spherical four dimensional dyonic black hole which represents a
wrapped fundamental string carrying arbitrary winding and momentum charges
along one cycle in the presence of KK-monopole and H-monopole charges
associated to another cycle. It is verified that after the inclusion of the
gravitational Chern-Simons corrections [hep-th/0608182], all the linear
alpha-prime corrections to the entropy for the supersymmetric dyon can be
reproduced by the inclusion of only the Gauss-Bonnet Lagrangian to the
supergravity approximation of the induced Lagrangian.
