We investigate the role of the pion in Covariant Density Functional Theory. Starting from conventional Relativistic Mean Field (RMF) theory with a non-linear coupling of the $sigma$-meson and without exchange terms we add pions with a pseudo-vector coupling to the nucleons in relativistic Hartree-Fock approximation. In order to take into account the change of the pion field in the nuclear medium the effective coupling constant of the pion is treated as a free parameter. It is found that the inclusion of the pion to this sort of density functionals does not destroy the overall description of the bulk properties by RMF. On the other hand, the non-central contribution of the pion (tensor coupling) does have effects on single particle energies and on binding energies of certain nuclei.
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