  Within the relativistic mean-field approach, we extend the Miyazaki model,
where the NN$\sigma$ and NN$\omega$ interactions are modified to suppress the
couplings between positive- and negative-energy states of a nucleon in matter.
Assuming appropriate density-dependence of the meson-nucleon couplings, we
study nuclear matter and finite nuclei. The model can reproduce the observed
properties of $^{16}$O and $^{40}$Ca well. We also examine if the model is
natural.
