We prove, in this article, that a ring R is a stable exchange ring if and only if so are all its Pierce stalks. If every Pierce stalks of R is artinian, then $1_R$ = u + $upsilon$ with u, $upsilon$ $in$ U(R) if and only if for any a $in$ R, there exist u, $upsilon$ $in$ U(R) such that a = u + $upsilon$. Furthermore, there exists u $in$ U(R) such that $1_R;{pm};u;in;U(R)$ if and only if for any a $in$ R, there exists u $in$ U(R) such that $a;{pm};u;in;U(R)$. We will give analogues to normal exchange rings. The root properties of such exchange rings are also obtained.