  We construct the most general gauge fixing and the associated Faddeev-Popov
ghost term for the SU(2) Yang-Mills theory, which leaves the global U(1) gauge
symmetry intact (i.e., the most general Maximal Abelian gauge). We show that
the most general form involves eleven independent gauge parameters. Then we
require various symmetries which help to reduce the number of independent
parameters for obtaining the simpler form. In the simplest case, the
off-diagonal part of the gauge fixing term obtained in this way is identical to
the modified maximal Abelian gauge term with two gauge parameters which was
proposed in the previous paper from the viewpoint of renormalizability.
  In this case, moreover, we calculate the beta function, anomalous dimensions
of all fields and renormalization group functions of all gauge parameters in
perturbation theory to one-loop order. We also discuss the implication of these
results to obtain information on low-energy physics of QCD.
