  We consider the algebra isomorphism found by Frenkel and Ding between the RLL
and the Drinfeld realizations of $U_q(\widehat{gl(2)})$. After we note that
this is not a Hopf algebra isomorphism, we prove that there is a unique Hopf
algebra structure for the Drinfeld realization so that this isomorphism becomes
a Hopf algebra isomorphism. Though more complicated, this Hopf algebra
structure is also closed, just as the one found previously by Drinfeld.
