Let
A
A
be a connected cochain differential graded (DG, for short) algebra. This note shows that
A
A
is a
0
0
-Calabi-Yau DG algebra if and only if
A
A
is a Koszul DG algebra and
T
o
r
A
0
(
k
A
,
A
k
)
\mathrm {Tor}_A^0(\Bbbk _A,{}_A\Bbbk )
is a symmetric coalgebra. Let
V
V
be a finite dimensional vector space and
w
w
a potential in
T
(
V
)
T(V)
. Then the minimal subcoalgebra of
T
(
V
)
T(V)
containing
w
w
is a symmetric coalgebra, which implies that a locally finite connected cochain DG algebra is
0
0
-CY if and only if it is defined by a potential
w
w
.