Asymptotic behaviors of zero modes of the massless Dirac operator H = α • D + Q(x) are discussed, where α = (α 1 , α 2 , α 3 ) is the triple of 4 × 4 Dirac matrices, D = 1/i Δ x and Q(x) = (q jk (x)) is a 4 × 4 Hermitian matrix-valued function with | q jk (x) | ≤ C « x» -p ,p > 1. We shall show that for every zero mode f, the asymptotic limit of |x| 2 f (x) as |x| → + ∞ exists. The limit is expressed in terms of the Dirac matrices and an integral of Q(x) f (x). © 2007 Springer.