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Both projectable and non-projectable versions of Horava-Lifshitz gravity faceserious challenges. In the non-projectable version, the constraint algebra isseemingly inconsistent. The projectable version lacks a local Hamiltonianconstraint, thus allowing for an extra scalar mode which can be problematic. Anew formulation of non-projectable Horava-Lifshitz gravity, naturally realizedas a representation of the master constraint algebra studied by loop quantumgravity researchers, is presented. This yields a consistent canonical theorywith first class constraints. It captures the essence of Horava-Lifshitzgravity in retaining only spatial diffeomorphisms (instead of full space-timecovariance) as the physically relevant non-trivial gauge symmetry; at the sametime the local Hamiltonian constraint needed to eliminate the extra mode isequivalently enforced by the master constraint.

New formulation of Horava-Lifshitz quantum gravity as a master constraint theory