  We study attractor mechanism in extremal black holes of Einstein-Born-Infeld
theories in four dimensions. We look for solutions which are regular near the
horizon and show that they exist and enjoy the attractor behavior. The
attractor point is determined by extremization of the effective potential at
the horizon. This analysis includes the backreaction and supports the validity
of non-supersymmetric attractors in the presence of higher derivative
interactions in the gauge field part.
