  We prove that every non-trivial structure of a rationally connected fibre
space (and so every structure of a Mori-Fano fibre space) on a general (in the
sense of Zariski topology) hypersurface of degree $M$ in the
$(M+1)$-dimensional projective space for $M\geq 14$ is given by a pencil of
hyperplane sections. In particular, the variety $V$ is non-rational and its
group of birational self-maps coincide with the group of biregular
automorphisms and is therefore trivial. The proof is based on the techniques of
the method of maximal singularities and the inversion of adjunction.
