Following S. Schwarz [3], a semigroup S is called a periodic semigroup, if every element of S has a finite order, that is, if, for every element a of S, the subsemigroup (a) = {a │ a, a^2, . . ., a^n, . . .} generated by a contains a finite number of different elements. Any strongly reversible periodic semigroup is the class sum of mutually disjoint unipotent semigroups. This theorem has been proved by K. Iseki [2]. The purpose of this note is to present a necessary and sufficient condition for a periodic semigroup to be a band of unipotent homogroups, and some relevant matters. Throughout the paper, S will denote a periodic semigroup.