  We prove that a generic (in the sense of Zariski topology) Fano complete
intersection $V$ of the type $(d_1,...,d_k)$ in ${\mathbb P}^{M+k}$, where
$d_1+...+d_k=M+k$, is birationally superrigid if $M\geq 7$, $M\geq k+3$ and
$\mathop{\rm max} \{d_i\}\geq 4$. In particular, on the variety $V$ there is
exactly one structure of a Mori fibre space (or a rationally connected fibre
space), the groups of birational and biregular self-maps coincide, $\mathop{\rm
Bir} V= \mathop{\rm Aut} V$, and the variety $V$ is non-rational. This fact
covers a considerably larger range of complete intersections than the result of
[J. reine angew. Math. {\bf 541} (2001), 55-79], which required the condition
$M\geq 2k+1$.
  The paper is dedicated to the memory of Eckart Viehweg.
