  A manifestly N=2 supersymmetric completion of the four-dimensional
Nambu-Goto-Born-Infeld action, which is self-dual with respect to
electric-magnetic duality, is constructed in terms of the abelian N=2
superfield strength W in the conventional N=2 superspace. A relation to the
known N=1 supersymmetric Born-Infeld action in N=1 superspace is established.
The action found can be considered either as the Goldstone action associated
with partial breaking of N=4 supersymmetry down to N=2, with the N=2 vector
superfield being a Goldstone field, or, equivalently, as the gauge-fixed
superfield action of a D-3-brane in flat six-dimensional ambient spacetime.
