We prove that if the p-reduced abelian group G is a special countable extension of its totally projective p-component of torsion G p and R is a perfect commutative unitary ring of prime characteristic p,then the group S(G) of all normed p-units in the group algebra RG modulo Gp,that is,S(G)/Gp,is totally projective.Our result strengthens both classical results obtained by May and Hill-Ullery.