  We improve Ottaviani's splitting criterion for vector bundles on a quadric
hypersurface and obtain the equivalent of the result by Rao, Mohan Kumar and
Peterson. Then we give the classification of rank 2 bundles without "inner"
cohomology on Q_n (n>3). It surprisingly exactly agrees with the classification
by Ancona, Peternell and Wisniewski of rank 2 Fano bundles.
