  We show that the Horava theory for the completion of General Relativity at UV
scales can be interpreted as a gauge fixed theory, and it can be extended to an
invariant theory under the full group of four-dimensional diffeomorphisms. In
this respect, although being fully relativistic, it results to be locally
anisotropic in the time-like and space-like directions defined by a family of
irrotational observers. We show that this theory propagates generically three
degrees of freedom: two of them are related to the four-dimensional
diffeomorphism invariant graviton (the metric) and one is related to a
propagating scalar mode. Finally, we note that in the present formulation,
matter can be consistently coupled to gravity.
