In this paper we introduce the notion of free product of formal series. Using this notion, we can characterize the free product of submonoids of \(A^*\) , where \(A^*\) is the free monoid generated by an alphabet A. Moreover given a set \(X\subseteq A^+\) , where \(A^+\) is the free semigroup generated by an alphabet A, we can characterize a partition of X by the free product of the formal series associated to the classes of the partition.