Let X be a smooth projective variety of dimension 2κ- 1 (κ ≥ 3) over the complex number field. Assume that fR: X → Y is a small contraction such that every irreducible component Ei of the exceptional locus of fR is a smooth subvariety of dimension κ. It is shown that each Ei is isomorphic to the κ-dimensional projective space pκ, the κ-dimensional hyperquadric surface Qκ in Pκ+1, or a linear Pκ-1-bundle over a smooth curve.