  The final state of the decay D0 --> pi+ pi- pi0 is analyzed in terms of
isospin eigenstates. It is shown that the final state is dominated by the
isospin-0 component. This suggests that isospin considerations may provide
insight into this and perhaps other $\Dz$-meson decay. We also discuss the
isospin nature of the nonresonant contribution in the decay, which can be
further understood by studying the decay D0 --> pi0 pi0 pi0.
