  We show that the super D3-brane action on $AdS_5 \times S^5$ background
recently constructed by Metsaev and Tseytlin is exactly invariant under the
combination of the electric-magnetic duality transformation of the worldvolume
gauge field and the SO(2) rotaion of N=2 spinor coordinates. The action is
shown to satisfy the Gaillard-Zumino duality condition, which is a necessary
and sufficient condition for a action to be self-dual. Our proof needs no gauge
fixing for the $\kappa$-symmetry.
