  The paper deals with a modified Godbillon-Vey class defined by Losik for
codimension-one foliations. This characteristic class takes values in the
cohomology of the second order frame bundle over the leaf space of the
foliation. The definition of the Reeb foliation depends upon two real functions
satisfying certain conditions. All these foliations are pairwise homeomorphic
and have trivial Godbillon-Vey class. We show that the modified Godbillon-Vey
is non-trivial for some Reeb foliations and it is trivial for some other Reeb
foliations. In particular, the modified Godbillon-Vey class can distinguish
non-diffeomorphic foliations and it provides more information than the
classical Godbillon-Vey class. We also show that this class is non-trivial for
some foliations on the two-dimensional surfaces.
