AS previous article if we give appropiatc Constraint to the gauge invariant Lagrangian of more general gauge group. The variation principle of the action convert to the variational problem with Subsidiary conditions

we consider the transformation properties of constrained system

The effecive Lagrangian which contains Lagrangian multiplier may has a mass term of the gauge mesons

The ctfective Lagrangian is invariant under the multiplier gauge transformatien.To use the path-integral formalism wo can give the quantizaton of massive yang- Mills fields which is invariant under the multiplier gauge transfotmaion.