\textit{K. S. S. Nambooripad} [Mem. Am. Math. Soc. 224 (1979; Zbl 0457.20051)] introduced the concept of a (regular) biordered set to abstractly characterize the set of idempotents of a regular semigroup. He also described the biordered sets associated with bands. The author gives an alternative description of those biordered sets which, in the words of the author, is ''easy to test and arises naturally by considering the representation of a biordered set'' introduced by him and \textit{T. E. Hall} [''Reconstructing some idempotent-generated semigroups from their biordered sets'' (to appear)].