  Kotschick and Morita recently discovered factorisations of characteristic
classes of transversally symplectic foliations that yield new characteristic
classes in foliated cohomology. We describe an alternative construction of such
factorisations and construct examples of topologically trivial foliated vector
bundles for which these characteristic classes are non-trivial. This shows that
the foliated cohomology classes of Kotschick and Morita carry information that
is not merely topological.
