  Let X be the blow-up of a smooth projective 4-fold Y along a smooth curve C
and let E be the exceptional divisor. Assume that X is a Fano manifold and has
an elementary extremal contraction $\phi: X \to Z$ of (3,1)-type such that E is
$\phi$-ample (recall that a contraction map for a 4-fold is called (3,1)-type
if the exceptional locus is a divisor and its image is a curve). We show that
if the exceptional divisor of $\phi$ is smooth, then Y is isomorphic to
$\mathbb{P}^{4}$ and C is an elliptic curve of degree 4.
