  The study of Majorana fermions is of great importance for the implementation
of a quantum computer. These modes are topologically protected and very stable.
It is now well known that a p-wave superconducting wire can sustain, in its
topological non-trivial phase, Majorana quasi-particles at its ends. Since this
type of superconductor is not found in nature, many methods have been devised
to implement it. Most of them rely on the spin-orbit interaction. In this paper
we study the superconducting properties of a two-band system in the presence of
antisymmetric hybridization. We consider inter-band attractive interactions and
also an attractive interaction in one of the bands. We show that
superconducting fluctuations with p-wave character are induced in the
non-interacting band due to the combined effects of inter-band coupling and
hybridization. In the case of a wire, this type of induced superconductivity
gives rise to four Majorana modes at its ends. The long range correlation
between the different charge states of these modes offers new possibilities for
the implementation of protected q-bits.
