  We show that the problem of ghosts in critical gravity and its higher
dimensional extensions can be resolved by giving dynamics to the symmetric rank
two auxiliary field existing in the action of these theories. These New
Bi-Gravities, at linear level around the AdS vacuum, are free of Boulware-Deser
ghost, kinetic ghost and tachyonic instability within the particular range of
parameters. Moreover, we show that the energy and entropy of AdS-Schwarzschild
black hole solutions of these new models are positive in the same range of
parameters. This may be the sign that these new models are also free of ghost
instabilities at the non-linear level.
