  We study the degrees of freedom in New General Relativity -- flat and metric
compatible family of theories -- around the Minkowski background in a gauge
invariant manner. First, we confirm the decoupling case, in which the theory
reduces to linearized gravity plus a massless KR field. We then show that,
unless they vanish, the vector modes of this theory will be ghosts. In
addition, we find two new branches of the theories, which are ghost-free and
propagate linearly two tensor modes and in one of the cases also a massless
scalar field. This shows that while the generic theory is ill-behaved, there
are three possible realizations of ghost-free cases, in contradiction to the
previous literature, which states that there is only one ghost-free theory in
addition to general relativity.
