In §1, for a topological ordered space X and an equivalence relation R on X, we shall study some sufficient conditions for X/R to be T_2-ordered. In §2, we shall investigate the necessary and suffieient condition of R for X/R to be T_2-0rdered, which is an analogue of a known fact in general topology. ( [1] §8 Proposition 8 or [2] Chapter 3 Theorem 11)