  We make a systematic study of the isospin symmetry of fragmentation functions
by taking decay contributions into account. We assume the isospin symmetry in
strong interactions and show that in the unpolarized case the isospin symmetry
is held for fragmentation functions of $\Lambda$ and only tiny violations are
allowed for other hadrons such as nucleon and pions due to the contributions
from weak decays. We present a rough estimate of the magnitudes of such
violations. In the polarized case, we show that the isospin symmetry violation
for $\Lambda$ production should be tiny and the recent Belle data on the
transverse polarization of $\Lambda$ can be reproduced if the isospin symmetry
is kept in the corresponding polarized fragmentation functions.
