  Quantum field theory in the near-horizon region of a black hole predicts the
existence of an infinite number of degenerate modes. Such a degeneracy is
regulated in the brick wall model by the introduction of a short distance
cutoff. In this Letter we show that states of the brick wall model with non
zero energy admit a further degeneracy for any given finite value of the
cutoff. The black hole entropy is calculated within the brick wall model taking
this degeneracy into account. Modes with complex frequencies however do not
exhibit such a degeneracy.
