  We perform an analysis of the ultraviolet divergences of the quantum
nonprojectable Horava gravity. We work the quantum field theory directly in the
Hamiltonian formalism provided by the Batalin-Fradkin-Vilkovisky quantization.
In this way the second-class constraints can be incorporated to the
quantization. A known local gauge-fixing condition leads to a local canonical
Lagrangian. Although the canonical fields acquire regular propagators,
irregular propagators persist for the field associated to the measure of the
second-class constraints. Loops can be formed with the irregular propagators
producing potentially dangerous subdivergences. We show that all these loops
cancel exactly between them due to a perfect matching between the propagators
and vertices of the fields and ghosts forming the loops. The rest of
divergences behaves similiarly to the projectable theory, they can be removed
by local counterterms. This result points to the renormalization of the
nonprojectable Horava theory.
