The so long made assumption, that a general closed-string vertex opera
tor V should be built as a product of left- and right-moving vertex op
erators, rests on the fact that the closed-string Fock spce is constru
cted as a tensor product of left- and right-moving open-string Fock sp
aces. In this letter we will relax this assumption by proving that fac
torization of closed-string vertices is a general rule.