  In previous work done by us and coworkers, we have been able to construct a
local, non-Abelian gauge invariant action with a mass parameter, based on the
nonlocal gauge invariant mass dimension two operator F1/D^2F. The
renormalizability of the resulting action was proven to all orders of
perturbation theory, in the class of linear covariant gauges. We also discussed
the perturbative equivalence of the model with ordinary massless Yang-Mills
gauge theories when the mass is identically zero. Furthermore, we pointed out
the existence of a BRST symmetry with corresponding nilpotent charge. In this
paper, we study the issue of unitarity of this massive gauge model. Firstly, we
provide a short review how to discuss the unitarity making use of the BRST
charge. Afterwards we make a detailed study of the most general version of our
action, and we come to the conclusion that the model is not unitary, as we are
unable to remove all the negative norm states from the physical spectrum in a
consistent way.
