  We consider a gravitating system of vanishing cosmological constant
consisting of an electromagnetic field and a scalar field coupled to the
Einstein tensor. A Reissner-Nordstr\"om black hole undergoes a second-order
phase transition to a hairy black hole of generally anisotropic hair at a
certain critical temperature which we compute. The no-hair theorem is evaded
due to the coupling between the scalar field and the Einstein tensor. Within a
first order perturbative approach we calculate explicitly the properties of a
hairy black hole configuration near the critical temperature and show that it
is energetically favorable over the corresponding Reissner-Nordstr\"om black
hole.
