  We examine the known Riemann curvature corrections to the supergravity action
at order $\alpha'^3$ under the T-duality transformations. Using the
compatibility of the action with the linear T-duality and with the S-matrix
calculations as guiding principles, we have found the couplings of four
$B$-field strengths and the couplings of two Riemann curvatures and two
$B$-field strengths at order $\alpha'^3$. Using the S-matrix calculations we
have also found new dilaton couplings in the string frame at this order.
