  We observe that the replacement of the Riemann curvature with the generalized
Riemann curvature into the corrections to the type II supergravity at order
$\alpha'^3$ which are in terms of the contractions of four Riemann curvatures
$R^4$, is not fully consistent with the S-matrix elements in the superstring
theory. In particular, they produce non-zero S-matrix elements for odd number
of B-field strengths which are not consistent with the string theory results.
Using the consistency of the couplings with the linear T-duality as a guiding
principle, we consider all T-duality invariant couplings and fix their
coefficients by requiring them to be consistent with the S-matrix elements. The
new Lagrangian density is then equivalent to the replacement of the generalized
Riemann curvature into the expression $t_8t_8R^4$.
