  A relation among the effective nucleon mass $M^*$, the incompressibility $K$
and the effective $\sigma$-meson mass $m_{\rm s}^*$ in nuclear matter is
studied by using the relativistic nuclear model. We found that there is a
strong correlation between $M^*$ and $m_{\rm s}^*$, while there is only a weak
correlation between $K$ and $m_{\rm s}^*$. At the normal density, $m_{\rm s}^*$
is smaller than the one at zero density, if $M^*$ is smaller than 0.8 times of
the nucleon mass at zero density. It is also found that the off-shell effective
mass $\mu_{\rm s}^*$ is related directly to $K$ and $M^*$ at the normal
density.
