A birational transformation f: P^n--> Z,where Z is a nonsingular variety of Picard number 1,is called a special birational transformation of type(a,b)if f is given by a linear system of degree a,its inverse is given by a linear system of degree b and the base locus S \subset P^n off is irreducible and nonsingular.Ill report a joint work with Jun-Muk Hwang on the classification of special birational transformations of type(2,1).