Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring Mn(R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is ...