  Recently, Horava and Melby-Thompson proposed in arXiv:1007.2410 a
nonrelativistic gravity theory with extended gauge symmetry that is free of the
spin-0 graviton. We propose a minimal substitution recipe to implement this
extended gauge symmetry which reproduce the results obtained by them. Our
prescription has the advantage of being manifestly gauge invariant and
immediately generalizable to other fields, like matter. We briefly discuss the
coupling of gravity with scalar and vector fields found by our method. We show
also that the extended gauge invariance in gravity does not force the value of
$\lambda$ to be $\lambda=1$ as originally claimed. However, the spin-0 graviton
is eliminated even for general $\lambda$.
