There are very few cases known of nonabelian groups G where the group
of central units of ZG, denoted Z(U(ZG)), is nontrivial and where the
structure of Z(U(ZG)), including a complete set of generator's, has be
en determined. In this note, we show that the central units of augment
ation I in the integral group ring ZA(5) form an infinite cycle group
[u], and we explicitly find the generator u.