  A characteristic class for deformations of foliations called the
Fuks-Lodder-Kotschick class (FLK class for short) is studied. It seems unknown
if there is a real foliation with non-trivial FLK class. In this article, we
show some conditions to assure the triviality of the FLK class. On the other
hand, we show that the FLK class is easily to be non-trivial for transversely
holomorphic foliations. We present an example and give a construction which
generalizes it.
