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We investigate unattractor behavior in non-extremal black holes inEinstein-Born-Infeld-Dilaton theory of gravity in four-dimensionalasymptotically flat spacetime. We obtain solutions which are non-singular nearthe horizon and dependent on the value of the dilaton field at the infinity,using perturbation method. It is shown that the value of the scalar field atthe horizon is determined by its asymptotic value and the charges carried bythe black hole. And we also find it is not true in general that the dilatonvalue at the horizon is a monotonically increasing function of the firstcoefficient of its series expansion in non-extremal Born-Infeld black holes.

Non-Supersymmetric Unattractors in Born-Infeld Black Holes