We associate with every anti-ordered set $((X,=,\neq),\alpha)$ with $\alpha\cap\alpha^{-1}=\emptyset$ a partial groupoid $((X,=,\neq),\cdot)$ in such a way that $(x,y)\in\alpha\Longleftrightarrow x\cdot y=y$ and $(x,y)\bowtie\alpha\Longleftrightarrow x\cdot y=x$ for two elements $x,y\in X$ such that $x\neq y$.