  We consider rotating topological black branes with one rotational parameter
in various dimensions. Also a general five-dimensional higher genus solution of
the Einstein equation with a negative cosmological constant which represents a
topological black brane with two rotational parameters is introduced. We find
out that the counterterms inspired by conformal field theory introduced by
Kraus, Larsen and Sieblink cannot remove the divergences in $r$ of the action
in more than five dimensions. We modify the counterterms by adding a curvature
invariant term to it. Using the modified counterterms we show that the $r$
divergences of the action, the mass, and the angular momentum densities of
these spacetimes are removed. We also find out in the limit of $m=0$ the mass
density of these spacetimes in odd dimensions is not zero.
