  The minimum of intersection numbers of the anti-canonical divisor with
rational curves on a Fano manifold is called pseudo-index. It is expected that
the intersection number of anti-canonical divisor attains to the minimum on an
extremal ray, i.e. there exists an extremal rational curve whose intersection
number with the anti-canonical divisor equals the pseudo-index. In this note,
we prove this for smooth Fano 4-folds having birational contractions.
