  Recently, a novel four-dimensional Gauss-Bonnet theory has been suggested as
a limiting case of the original $D$-dimensional theory with singular
Gauss-Bonnet coupling constant $\alpha\rightarrow\alpha/(D-4)$. The theory is
proposed at the level of field equations. Here we analyse this theory at the
level of action. We find that the on-shell action and surface terms split into
parts, one of which does not scale like $(D-4)$. The limiting $D\rightarrow4$
procedure, therefore, gives unphysical divergences in the on-shell action and
surface terms in four dimensions. We further highlight various issues related
to the computation of counterterms in this theory.
