A ring with involution * is called *-clean if each of its elements is the sum of a unit and a projection (*-invariant idempotent). In this paper, we consider the group algebras of the dihedral groups D-2n, and the generalized quaternion groups Q(2n) with standard involution *. For the non-semisimple group algebra case, we characterize the *-cleanness of RD2pk with a prime p is an element of J(R), and RD2n with 2 is an element of J(R), where R is a commutative local ring. For the non-semisimple group algebra case, we investigate when KG is *-clean, where K is the field of rational numbers Q or a finite field F-q and G - D-2n or G - Q(2n).
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