New Branches of Non-supersymmetric Attractors in N=2 Supergravity

In this paper we analyse non-supersymmetric single centred extremal black hole solutions in N=2 supergravity theory coupled to $n$ vector multiplets with purely cubic pre-potential in four dimensions. We consider the algebraic attractor equations in their most general form at the black hole horizon. We explicitly construct a new class of solutions for these attractor equations. These solutions are characterised by a set of involutory matrices. These involutions are obtained from a constraint involving the parameters in the pre-potential and generate new attractor points in the moduli space.