  There is a conjecture in the literature that indicates the tree-level
S-matrix elements of graviton become symmetric under the $SL(2,Z)$
transformation after including the loops and the nonperturbative effects. Using
the Ward identity corresponding to the global S-duality transformations, this
conjecture can be extended to other S-matrix elements as well. While the
$SL(2,Z)$ transformation on the background dilaton is nonlinear, the Ward
identity dictates the S-duality transformations on external states should be
the linearized $SL(2,R)$ transformations. We examine in details various
S-matrix elements involving massless closed string and/or open string vertex
operators on the world volume of D$_3$-brane in favor of this conjecture.
