Let
(
A
,
d
)
(A,d)
be a differential graded algebra of finite type, if
H
∗
(
A
)
H^*(A)
is a Gorenstein graded algebra, then so is
A
A
. The purpose of this paper is to prove the converse under some mild hypotheses. We deduce a new characterization of Poincaré duality spaces as well as spaces with a nonzero evaluation map.