  Massive gravity can be described by adding to the Einstein-Hilbert action a
function V of metric components. By using the Hamiltonian canonical analysis,
we find the most general form of V such that five degrees of freedom propagate
non perturbatively. The construction is based on a set of differential
equations for $V$, that remarkably can be solved in terms of two arbitrary
functions. Besides recovering the known "Lorentz invariant" massive gravity
theory, we find an entirely new class of solutions, with healthy features on
the phenomenological side, in particular they are weakly coupled in the solar
system and have a high ultraviolet cutoff Lambda_2=(m M_pl)^(1/2), where m is
the graviton mass scale.
