Let us adduce some definitions: If a recursively enumerable (r.e.) set A is a disjoint union of two sets B and C, then we say that B, C is a r.e. splitting of A. A r.e. set A is tt-mitotic (btt-mitotic) if there is a r.e. splitting (B,C) of A such that the sets B and C both belong to the same tt- ( btt-) degree of unsolvability, as the set A. In this paper it is proved, that there exists a tt-complete set, which is tt-mitotic, but not btt-mitotic. Moreover, the constructed set A is, indeed, q-complete.