Let $G=(V,E))$ be a directed graph. A $2$-twinless block in $G$ is maximal vertex set $B\subseteq V$ of size at least $2$ such that for each pair distinct vertices $x,y \in B$, and $w\in V\setminus\left\lbrace x,y \right\rbrace $, the $x,y$ are same twinless strongly connected component $G\setminus\left \lbrace w $. In this paper we present algorithms computing blocks