  Interactions in bimetric theory, which can describe gravity in the presence
of an extra spin-2 field, are severely constrained by the requirement of the
absence of the Boulware-Deser ghost instability. Recently an interesting new
matter coupling was proposed in terms of a composite metric but it was claimed
to reintroduce the ghost. In this paper we carry out a nonlinear Hamiltonian
analysis of this new matter coupling and show that it is indeed ghost-free. The
analysis involves using a new set of variables that naturally appear in the
relation between the metric and vielbein formulations of bimetric theory. In
terms of these variables we show that the new matter coupling does not reduce
the number of constraints in bimetric theory and hence does not reintroduce the
Boulware-Deser ghost.
