Let $\Cal{T}_n$ be the full transformation semigroup on the set $\{1,2,\ldots,n\}$ and ${\rm Sing}_n$ the singular part of $\Cal{T}_n$, consisting of all noninvertible transformations. For a group $G$ and a semigroup $S$, the wreath product of $G$ by $S$, denoted by $G\wr S$, is defined by a semidirect product $G^n\rtimes S$. In this paper, the authors find a presentation for the wreath product $G\wr{\rm Sing}_2$ for an arbitrary group $G$ in terms of the idempotent generating set. To prove this main result, a characterization of an element in ${\rm Sing}_n$ and a presentation of ${\rm Sing}_n$ are useful. Finally, they show that the generating relations in that representation for the wreath product $G\wr{\rm Sing}_2$ cannot be reduced.