  A new type of gauge fixing of the Coulomb gauge domain wall fermion system
that reduces the fluctuation of the effective running coupling and the
effective mass of arbitrary momentum direction including the region outside the
cylinder cut region is proposed and tested in the $16^3\times 32\times 16$
gauge configurations of RBC/UKQCD collaboration.
  The running coupling at the lowest momentum point does not show infrared
suppression and compatible with the experimental data extracted from the JLab
collaboration. The source of the fluctuation of the effective mass near
momentum $p=$0.6GeV region is expected to be due to the domain wall fermion
zero modes.
