  Upon examining the effective action of the heterotic string theory at order
$\alpha'^2$, an inconsistency between the Chern-Simons coupling $\Omega^2$ and
T-duality has been discovered. To address this issue, we introduce 60
parity-even independent geometrical couplings involving the $B$-field, metric,
and dilation at the same order, each with arbitrary coefficients. To ensure the
invariance of these couplings under T-duality, we consider the Miessner action
for the couplings at order $\alpha'$ and rigorously determine the coefficients
of the 60 couplings in terms of the Chern-Simons coupling. Notably, it is found
that the coefficients of the Riemann cubed terms must be zero, which aligns
with the results of S-matrix calculations. Additionally, the parity odd
couplings at order $\alpha'^2$ are obtained through T-duality. Overall, our
analysis successfully resolves the inconsistency between the Chern-Simons
coupling and T-duality, providing a more comprehensive understanding of the
behavior of the heterotic string theory at order $\alpha'^2$.
