| The main result of this paper is as follows : Let X be a smooth projective variety of dimension 7 which has a small contraction map f:X→Y. Assume that all uniruled components Ei of the exceptional locus E of f are smooth subvarieties and have the dimension 4 , and the normal bundle NE1/x(?)OE1(-1) , then Ei(?)p4 or Q4, where p4 is the complex projective space of dimension 4, Q4 is a hyperquadric surface in p5. Moreover, the flip f+:X→Y of the small contraction f exists. |