  We explore the properties of non-BPS multi-centre extremal black holes in
ungauged N=2 supergravity coupled to n_v vector multiplets, as described by
solutions to the composite non-BPS linear system. After setting up an explicit
description that allows for arbitrary non-BPS charges to be realised at each
centre, we study the structure of the resulting solutions. Using these results,
we prove that the binding energy of the composite is always positive and we
show explicitly the existence of walls of marginal stability for generic
choices of charges. The two-centre solutions only exist on a hypersurface of
dimension n_v+1 in moduli space, with an n_v-dimensional boundary, where the
distance between the centres diverges and the binding energy vanishes.
