  The specific nonlinear vector $\sigma$-model coupled to Einstein gravity is
investigated. The model arises in the studies of the gravitating matter in
non-commutative geometry. The static spherically symmetric spacetimes are
identified by direct solving of the field equations. The asymptotically flat
black hole with the ``non-commutative'' vector hair appears for the special
choice of the integration constants, giving thus another counterexample to the
famous ``no-hair'' theorem.
