  A normal projective variety X is called Fano if a multiple of the
anticanonical Weil divisor, -K_X, is an ample Cartier divisor, the index of a
Fano variety is the number i(X):=sup{t: -K_X= tH, for some ample Cartier
divisor H}. Mukai announced, the classification of smooth Fano manifolds X of
index i(X)=n-2, under the assumption that the linear system |H| contains a
smooth divisor. In this paper we prove that this assumption is always
satisfied. Therefore the result of Mukai provide a complete classification of
smooth Fano n-folds of index $i(X)=n-2$, Mukai manifolds.
