  Using the linear T-dual ward identity associated with the NSNS gauge
transformations, some RR couplings on D$_p$-branes have been found at order
$O(\alpha'^2)$. We examine the $C^{(p-1)}$ couplings with the S-matrix elements
of one RR, one graviton and one antisymmetric B-field vertex operators. We find
the consistency of T-dual S-matrix elements and explicit results of scattering
string amplitude and show that the string amplitude reproduces these couplings
as well as some other couplings. This illustration is found for $C^{(p-3)}$
couplings in the literature which is extended to the $C^{(p-1)}$ couplings in
this paper.
