  Starting with a bare nucleon-nucleon interaction, for the first time the full
relativistic Brueckner-Hartree-Fock equations are solved for finite nuclei in a
Dirac-Woods-Saxon basis. No free parameters are introduced to calculate the
ground-state properties of finite nuclei. The nucleus $^{16}$O is investigated
as an example. The resulting ground-state properties, such as binding energy
and charge radius, are considerably improved as compared with the
non-relativistic Brueckner-Hartree-Fock results and much closer to the
experimental data. This opens the door for \emph{ab initio} covariant
investigations of heavy nuclei.
