  We have presented non-Abelian dual superconductivity picture in the SU(3)
Yang-Mills(YM) theory, and shown evidences such as the restricted U(2)-field
dominance and the non-Abelian magnetic monopole dominance in the string
tension. To establish the dual superconductivity picture, the dual Meissner
effect in Yang-Mills theory must be examined, and we also presented the
evidence of non-Abelian dual Meissner effect by measuring chromo-electric flux
tube in the last lattice conferences.
  In this talk, by applying a new formulation of the YM theory on a lattice,
the we further investigate the non-Abelian dual Meissner effect for SU(3) YM
theory through correlation function. We examine non-abelian magnetic monopole
currents as well as color flux created by the quark-antiquark source.
