  In this paper, we show that the spin-0 gravitons appearing in Horava-Lifshitz
gravity without the projectability condition can be eliminated by extending the
gauge symmetries of the foliation-preserving diffeomorphisms to include a local
U(1) symmetry. As a result, the problems of stability, ghost, strong coupling,
and different speeds in the gravitational sector are automatically resolved. In
addition, with the detailed balance condition softly breaking, the number of
independent coupling constants can be significantly reduced (from more than 70
down to 15), while the theory is still UV complete and possesses a healthy IR
limit, whereby the prediction powers of the theory are considerably improved.
The strong coupling problem in the matter sector can be cured by introducing an
energy scale $M_{*}$, so that $M_{*} < \Lambda_{\omega}$, where $M_{*}$ denotes
the suppression energy of high order derivative terms, and $\Lambda_{\omega}$
the would-be strong coupling energy scale.
