  The variational Lie derivative of classes of forms in the Krupka's
variational sequence is defined as a variational Cartan formula at any degree,
in particular for degrees lesser than the dimension of the basis manifold. As
an example of application we determine the condition for a
Noether--Bessel-Hagen current, associated with a generalized symmetry, to be
variationally equivalent to a Noether current for an invariant Lagrangian. We
show that, if it exists, this Noether current is exact on-shell and generates a
canonical conserved quantity.
