  We provide an auxiliary field formulation of the full ghost-free bimetric
theory which avoids the explicit presence of a square-root matrix in the
action. This description always allows for a branch of solutions where the
auxiliary fields can be integrated out to give back the ghost-free theory. For
certain parameter regions the two formulations are dynamically equivalent, but
in the general case another branch of solutions also exists. We show that this
second branch, with certain restrictions on the parameters of the theory, is
dynamically equivalent to Eddington-inspired Born-Infeld gravity. This
establishes a definite connection between two seemingly unrelated theories of
modified gravity.
