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We observe that the replacement of the Riemann curvature with the generalizedRiemann 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 superstringtheory. In particular, they produce non-zero S-matrix elements for odd numberof 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 guidingprinciple, we consider all T-duality invariant couplings and fix theircoefficients by requiring them to be consistent with the S-matrix elements. Thenew Lagrangian density is then equivalent to the replacement of the generalizedRiemann curvature into the expression $t_8t_8R^4$.

Generalized Riemann curvature corrections to type II supergravity