  Using the formalism of noncommutative geometric gauge theory based on the
superconnection concept, we construct a new type of vector gauge theory
possessing a shift-like symmetry and the usual gauge symmetry. The new
shift-like symmetry is due to the matrix derivative of the noncommutative
geometric gauge theory, and this gives rise to a mass term for the vector field
without introducing the Higgs field. This construction becomes possible by
using a constant one form even matrix for the matrix derivative, for which only
constant zero form odd matrices have been used so far. The fermionic action in
this formalism is also constructed and discussed.
