  We analyze the gauge symmetry of a topological mass generating action in four
dimensions which contains both a vector and a second rank antisymmetric tensor
fields. In the Abelian case, this system induces an effective mass for the
vector gauge field via a topological coupling $B \wedge F$ in the presence of a
kinetic term for the antisymmetric tensor field $B$, while maintaining a gauge
symmetry. On the other hand, for the non-Abelian case the $B$ field does not
have a gauge symmetry unless an auxiliary vector field is introduced to the
system. We analyze this change of symmetry in the Faddeev-Jackiw formalism, and
show how the auxiliary vector field enhances the symmetry. At the same time
this enhanced gauge symmetry becomes reducible. We also show this phenomenon in
this analysis.

High Energy Physics - Theory