  In this short note, we have generalized and constructed gravity solutions
with two "exponents" {\it a la} Kachru, Liu and Mulligan. The coordinate system
that is used to construct the gravity solution is useful when $b$ vanishes. It
means we can describe the theory having only the temporal scale invariance
apart from the combination of both temporal and spatial scale invariance. The
two point correlation function of the scalar field in the mass less limit is
computed in a special case that is $a/b=2$.
