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 $2��$-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 $2��$ 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$��$ and 4$��$ contributions are negligible except in $^1S_0$ and $^3P_2$.

12 pages, RevTex, 14 figures