  Based upon the Bonn meson-exchange-model for the nucleon-nucleon ($NN$)
interaction, we calculate the charge-independence breaking (CIB) of the $NN$
interaction due to pion-mass splitting. Besides the one-pion-exchange (OPE), we
take into account the $2\pi$-exchange model and contributions from three and
four irreducible pion exchanges. We calculate the CIB differences in the
$^1S_0$ effective range parameters as well as phase shift differences for
partial waves up to total angular momentum J=4 and laboratory energies below
300 MeV. We find that the CIB effect from OPE dominates in all partial waves.
However, the CIB effects from the $2\pi$ model are noticable up to D-waves and
amount to about 40% of the OPE CIB-contribution in some partial waves, at 300
MeV. The effects from 3$\pi$ and 4$\pi$ contributions are negligible except in
$^1S_0$ and $^3P_2$.
