  There is an evidence that the N=2 Born-Infeld theory with spontaneously
broken N=4 supersymmetry exhibits self-duality. We perform a further check of
this hypothesis by constructing a new representation for the N=2 Born-Infeld
action through the auxiliary chiral superfield U. In such a formulation,
self-duality is equivalent to U(1) invariance of the U interaction. We
explicitly calculate the auxiliary interaction up to the 10th order and show
its U(1) duality invariance, thus proving that the original action is self-dual
to the same order. We also suggest a new method of recursive computation of the
N=2 Born-Infeld action in the standard formulation, based solely on the
nonlinear realization of the N=4 central charge on the N=2 superfield strengths
W, \bar W.
