  We have studied the influences of isospin symmetry breaking of
nucleon-nucleon interaction on the various properties of asymmetrical nuclear
matter and $\beta$-stable matter. For asymmetrical nuclear matter, it is found
that by including this isospin symmetry breaking, the changes of bulk
properties increase by increasing both density and asymmetry parameter.
However, these effects on the total energy and equation of state of
$\beta$-stable matter are ignorable. For asymmetrical nuclear matter, the
validity of the empirical parabolic law in the isospin symmetry breaking case
is shown. It is observed that the isospin symmetry breaking of nucleon-nucleon
interaction affects the $\beta$-equilibrium conditions in $\beta$-stable
matter.
