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 construct explicit examples of the Reeb foliations that are not diffeomorphic. For this purpose we show that a modified Godbillon-Vey class defined by Losik is non-trivial for some Reeb foliations and trivial for some other Reeb foliations. This characteristic class takes values in the second order frame bundle of the leaf space of the foliation. This is a joint work with Ya. Bazaikin and P. Gumenyuk.