  We construct an action which is invariant under the foliation preserving
diffeomorphism from the Einstein Hilbert action. Starting from the Einstein
Hilbert action, we introduce the gauge invariance under the anisotropic
rescaling by using the St\"uckelberg method. We then introduce the gauge field
corresponds to the anisotropic rescaling, and the St\"uckelberg field turns out
to be the Nambu-Goldstone boson. The Nambu-Goldstone boson, however, is not
completely eaten by the massive gauge field and the Nambu-Goldstone boson can
be integrated out from the action. Then the resultant action is a
Horava-Lifshitz type action which contains $R^3$ term.
