  In this work we studied the higher order gravity model which corresponds to
Hassan-Rosen ghost-free bi-gravity. To do this we absorb one of the metrics in
bi-gravity model in favor of the other metric in a recursive way. For the
second (recursion) step we get conformal gravity same as what has been done in
the literature. We generalize this idea by calculating up to the fourth order
gravity. To reach to a ghost-free higher order gravity we need to go to
infinite-derivative order gravity but we can see our model as an effective
theory. So adding higher order terms results in wider range of validity of our
model. We emphasize that graviton mass controls the validity of perturbative
approach.
