  It is proved, that, in order to avoid the ghost mode in bigravity theory, it
is sufficient to impose four conditions on the potential of interaction of the
two metrics. First, the potential should allow its expression as a function of
components of the two metrics' 3+1 decomposition. Second, the potential must
satisfy the first order linear differential equations which are necessary for
the presence of four first class constraints in bigravity. Third, the potential
should be a solution of the Monge-Ampere equation, where the lapse and shift
are considered as variables. Fourth, the potential must have a nondegenerate
Hessian in the shift variables. The proof is based on the explicit derivation
of the Hamiltonian constraints, the construction of Dirac brackets on the base
of a part of these constraints, and calculation of other constraints' algebra
in these Dirac brackets. As a byproduct, we prove that these conditions are
also sufficient in the massive gravity case.
