Each quasi-antiorder $\tau$ on anti-ordered semigroup $S$ induces anti-congruence $q$ on $S$ such that $S/q$ is an ordered semigroup under anti-order induced by $\tau$. In this note we prove that the converse of this statement also holds: Each anti-congruence $q$ on a semigroup $(S,=,\neq,\cdot)$ such that $S/q$ is an anti-ordered semigroup induces a quasi-antiorder on $S$.