  The general structure of trace anomaly, suggested recently by Deser and
Shwimmer, is argued to be the consequence of the Wess-Zumino consistency
condition. The response of partition function on a finite Weyl transformation,
which is connected with the cocycles of the Weyl group in $d=2k$ dimensions is
considered, and explicit answers for $d=4,6$ are obtained. Particularly, it is
shown, that addition of the special combination of the local counterterms leads
to the simple form of that cocycle, quadratic over Weyl field $\sigma$, i.e.
the form, similar to the two-dimensional Lioville action. This form also
establishes the connection of the cocycles with conformal-invariant operators
of order $d$ and zero weight. Beside that, the general rule for transformation
of that cocycles into the cocycles of diffeomorphisms group is presented.
