  We study the four-dimensional Einstein-Yang-Mills black hole in the presence
of Dirac fermion field. Assuming a spherically symmetric static asymptotically
flat black hole spacetime we consider both massless and massive fermion fields.
The (4+1)-dimensional Einstein-Yang-Mills system effectively reducing to
Einstein-Yang-Mills-Higgs-dilaton model, was also taken into account. One finds
that fermion vacuum leads to the destruction of black holes in question.
