  A generalization of the Mattis-Nam model (J.Math.Phys., 13 (1972), 1185),
which takes into account a correlated hopping and pairing of electrons, is
proposed, its exact solution is obtained. In the framework of the model the
stability of the zero energy Majorana fermions localized at the boundaries is
studied in the chain in which electrons interact through both the on-site
Hubbard interaction and the correlated hopping and pairing. The ground-state
phase diagram of the model is calculated, the region of existence of
topological states is determined. It is shown that low-energy excitations
destroy bonds between electrons in the chain, leading to an insulator state.
