  Recently it has been speculated that the S-matrix elements satisfy the Ward
identity associated with the T-duality. This indicates that a group of S-matrix
elements is invariant under the linear T-duality transformations on the
external states. If one evaluates one component of such T-dual multiplet, then
all other components may be found by the simple use of the linear T-duality.
The assumption that fields must be independent of the Killing coordinate,
however, may cause, in some cases, the T-dual multiplet not to be gauge
invariant. In those cases, the S-matrix elements contain more than one T-dual
multiplet which are intertwined by the gauge symmetry.
  In this paper, we apply the T-dual Ward identity on the S-matrix element of
one RR $(p-3)$-form and two NSNS states on the world volume of a D$_p$-brane to
find its corresponding T-dual multiplet. In the case that the RR potential has
two transverse indices, the T-dual multiplet is gauge invariant, however, in
the case that it has one transverse index the multiplet is not gauge invariant.
We find a new T-dual multiplet in this case by imposing the gauge symmetry.
  We show that the multiplets are reproduced by explicit calculation, and their
low energy contact terms at order $\alpha'^2$ are consistent with the existing
couplings in the literature.
