  Using relativistic Hartree-Fock (RHF) approximation, we study the effect of
Fock terms on the nuclear properties not only around the saturation density,
$\rho_{0}$, but also at higher densities. In particular, we investigate how the
momentum dependence due to the exchange contribution affects the nuclear
symmetry energy and its slope parameter, using the Lorentz-covariant
decomposition of nucleon self-energies in an extended version of the RHF model,
in which the exchange terms are adjusted so as to reproduce the single-nucleon
potential at $\rho_{0}$. We find that the Fock contribution suppresses the
kinetic term of nuclear symmetry energy at the densities around and beyond
$\rho_{0}$. It is noticeable that not only the isovector-vector ($\rho$) meson
but also the isoscalar mesons ($\sigma, \omega$) and pion make significant
influence on the potential term of nuclear symmetry energy through the exchange
diagrams. Furthermore, the exchange contribution prevents the slope parameter
from increasing monotonically at high densities.
