  This paper is intended to study diffeomorphism invariance and diffeomorphism
generation in the modified theory of gravity proposed by Horava. Firstly, we
demonstrate that the theory does not lose diffeomorphism invariance due to the
parameter $\lambda$, as it was previously believed. However, we show that the
presence of terms containing the Levi-Civita symbol in the original proposal of
Horava makes the theory diffeomorphism dependent. By neglecting such terms,
what returns fully diffeomorphism invariance to the action, we obtain the
equations of motion. Secondly, in the Hamiltonian formalism, we calculate the
transformations generated by some of the constraints of the theory. Then, we
prove that all diffeomorphisms of General Relativity are generated, on the
energy shell, by the constraints of the Horava-Lifshitz gravity.
