  The aim of this paper is to elucidate the relationship between the Gorenstein
Rees algebra $\R(I):=\bigoplus_{i\ge 0}I^i$ of an ideal $I$ in a complete
Noetherian local ring $A$ and the graded canonical module of the extended Rees
algebra $\R'(I):=\bigoplus_{i\in\Z}I^i$. It is known that the Gorensteinness of
$\R(I)$ is closely related to the property of the graded canonical module of
the associated graded ring $\G(I):=\bigoplus_{i\ge 0}I^i/I^{i+1}$. However,
there appears to be a shortage of satisfactory references analyzing the
relationship between $\R(I)$ and $\R'(I)$ unless the ring $\G(I)$ is
Cohen-Macaulay. This paper provides a characterization of the Gorenstein
property of $\R(I)$ using the graded canonical module of $\R'(I)$ without
assuming that the base ring $A$ is Cohen-Macaulay. Applying our criterion, we
demonstrate that a certain Kawasaki's arithmetic Cohen-Macaulayfication becomes
a Gorenstein ring when $A$ is a quasi-Gorenstein local ring with finite local
cohomology.
