In this paper, it will be generalized the notion of hypergroups of type U on the right to ternary hypergroups of type U on the right and some of their properties will be investigated. We will determine all ternary hypergroups of size 2 and 3. Quotient ternary hypergroups of type U on the right, by defining a regular relation, are considered and it will be proved that arisen ternary hypergroup is right reversible.