  A new approximate solution of vacuum and stationary Einstein field equations
is obtained. This solution is constructed by means of a power series expansion
of the Ernst potential in terms of two independent and dimensionless parameters
representing the quadrupole and the angular momentum respectively. The main
feature of the solution is a suitable description of small deviations from
spherical symmetry through perturbations of the static configuration and the
massive multipole structure by using those parameters. This quality of the
solution might eventually provide relevant differences with respect to the
description provided by the Kerr solution.
