  Asymptotic behaviors of zero modes of the massless Dirac operator
$H=\alpha\cdot D + Q(x)$ are discussed, where
  $\alpha= (\alpha_1, \alpha_2, \alpha_3)$ is the triple of $4 \times 4$ Dirac
matrices, $ D=\frac{1}{i} \nabla_x$, and $Q(x)=\big(q_{jk} (x) \big)$ is a
$4\times 4$ Hermitian matrix-valued function with
  $| q_{jk}(x) | \le C < x >^{-\rho} $, $\rho >1$.
  We shall show that for every zero mode $f$, the asymptotic limit of
$|x|^2f(x)$ as $|x| \to +\infty$ exists. The limit is expressed in terms of an
integral of $Q(x)f(x)$.
