  We consider dilaton--axion gravity interacting with $p\;\, U(1)$ vectors
($p=6$ corresponding to $N=4$ supergravity) in four--dimensional spacetime
admitting a non--null Killing vector field. It is argued that this theory
exibits features of a ``square'' of vacuum General Relativity. In the
three--dimensional formulation it is equivalent to a gravity coupled
$\sigma$--model with the $(4+2p)$--dimensional target space
$SO(2,2+p)/(SO(2)\times SO(2+p))$. K\"ahler coordinates are introduced on the
target manifold generalising Ernst potentials of General Relativity. The
corresponding K\"ahler potential is found to be equal to the logarithm of the
product of the four--dimensional metric component $g_{00}$ in the Einstein
frame and the dilaton factor, independently on presence of vector fields. The
K\"ahler potential is invariant under exchange of the Ernst potential and the
complex axidilaton field, while it undergoes holomorphic/antiholomorphic
transformations under general target space isometries. The ``square'' property
is also manifest in the two--dimensional reduction of the theory as a matrix
generalization of the Kramer--Neugebauer map.
