  We relax one of the requirements for topological quantum computation with
Majorana fermions. Topological quantum computation was discussed so far as
manipulation of the wave function within degenerate many body ground state. The
simplest particles providing degenerate ground state, Majorana fermions, often
coexist with extremely low energy excitations, so keeping the system in the
ground state may be hard. We show that the topological protection extends to
the excited states, as long as the Majorana fermions do not interact neither
directly, nor via the excited states. This protection relies on the fermion
parity conservation, and so it is generic to any implementation of Majorana
fermions.
