We study analytically the evolution of massless Dirac fields in the background of the Schwarzschild black hole. It is shown that although the quasinormal frequencies are the same for opposite chirality with the same |k|, we can differentiate neutrinos from anti-neutrinos in evolution of the massless Dirac fields provided we know both stages for the quasinormal modes and the power-law tail behavior since the decay rate of the neutrinos is described by t-(2|k|+1) while anti-neutrinos is t-(2|k|+3).