It is known that if all proper ideals in a non-reduced ring have no zero- divisors, then the ring is simple. In this paper, we use the concept of  *-reversible elements and then prove that if a ring with involution is not reduced and all *-proper ideals do not have any *-reversible elements, then R is *-simple. But if R is reduced and all *-proper ideals do not have any *-reversible element, then R is a direct sum of *-simple rings.

*-reversible rings, *-reversible elements, *-simple rings.