  We revisit the issue that the Noether current associated with a local scale
symmtery, or equivalently the Weyl symmetry, identically vanishes. Based on
only the second Noether theorem for a local symmetry, we prove that the Noether
current associated with the Weyl symmetry is in general vanishing in any Weyl
invariant gravitational theories in four dimensional Riemannian geometry. We
also clarify the reason: The Weyl transformation is non-dynamical in the sense
that it does not contain the derivative term of the transformation parameter as
opposed to the conventional gauge transformation. Finally, we apply this result
to a quantum theory of a general Weyl invariant gravity and derive currents
associated with choral symmetry, which is the $IOSp(10|10)$ supersymmetry.
