  We consider a recently proposed two-dimensional Abelian model for a Hodge
theory, which is neither a Witten type nor a Schwarz type topological theory.
It is argued that this model is not a good candidate for a Hodge theory since,
on-shell, the BRST Laplacian vanishes. We show, that this model allows for a
natural extension such that the resulting topological theory is of Witten type
and can be identified with the twisted N=16, D=2 super Maxwell theory.
Furthermore, the underlying basic cohomology preserves the Hodge-type structure
and, on-shell, the BRST Laplacian does not vanish.
