Let R be an exchange ring with primitive factors artinian. We prove that there exists a u. U(R) such that 1 R ± u . U(R), if and only if for any a. R, there exists a u . U(R) such that a ± u . U(R). Furthermore, we prove that, for any A . M n (R)(n . 2), there exists a U . GL n (R) such that A ± U . GL n (R)