  We analyze the ghost issue in the recently proposed models of non-linear
massive gravity in the ADM formalism. We show that, in the entire two-parameter
family of actions, the Hamiltonian constraint is maintained at the complete
non-linear level and we argue for the existence of a non-trivial secondary
constraint. This implies the absence of the pathological Boulware-Deser ghost
to all orders. To our knowledge, this is the first demonstration of the
existence of a consistent theory of massive gravity at the complete non-linear
level, in four dimensions.
