  In the present paper, non-singular Morse-Smale flows on closed orientable
3-manifolds under the assumption that among the periodic orbits of the flow
there is only one saddle one and it is twisted are considered. An exhaustive
description of the topology of such manifolds is obtained. Namely, it has been
established that any manifold admitting such flows is either a lens space, or a
connected sum of a lens space with a projective space, or Seifert manifolds
with base homeomorphic to sphere and three singular fibers. Since the latter
are simple manifolds, the result obtained refutes the result that among simple
manifolds, the considered flows admit only lens spaces.
