  The finiteness condition of renormalization gives a restriction on the form
of the gravitational action. By reconsidering the Hathrell's RG equations for
massless QED in curved space, we determine the gravitational counterterms and
the conformal anomalies as well near four dimensions. As conjectured for
conformal couplings in 1970s, we show that at all orders of the perturbation
they can be combined into two forms only: the square of the Weyl tensor in $D$
dimensions and $E_D=G_4 +(D-4)\chi(D)H^2 -4\chi(D) \nabla^2 H$, where $G_4$ is
the usual Euler density, $H=R/(D-1)$ is the rescaled scalar curvature and
$\chi(D)$ is a finite function of $D$ only. The number of the dimensionless
gravitational couplings is also reduced to two. $\chi(D)$ can be determined
order by order in series of $D-4$, whose first several coefficients are
calculated. It has a universal value of $1/2$ at $D=4$. The familiar ambiguous
$\nabla^2 R$ term is fixed. At the $D \to 4$ limit, the conformal anomaly $E_D$
just yields the combination $E_4=G_4-2\nabla^2 R/3$, which induces Riegert's
effective action.
