  From the Levi's Theorem it is known that every finite dimensional Lie algebra
over a field of characteristic zero is decomposed into semidirect sum of
solvable radical and semisimple subalgebra. Moreover, semisimple part is the
direct sum of simple ideals. In \cite{Bar} the Levi's theorem is extended to
the case of Leibniz algebras. In the present paper we investigate the
semisimple Leibniz algebras and we show that the splitting theorem for
semisimple Leibniz algebras is not true. Moreover, we consider some special
classes of the semisimple Leibniz algebras and find a condition under which
they decompose into direct sum of simple ideals.
