  In this paper we study flatness of the restriction on some special subgerms
(e.g. the reduction and the unmixed part) of the total space of a flat morphism
over a smooth base space. We give a relationship between reducedness of the
total space and that of the generic fibers of a flat morphism over a reduced
Cohen-Macaulay base space. Moreover, we study flatness of the composition of a
flat morphism over a smooth base space and the normalization of the total space
of that morphism.
