In this paper we introduce the concept of [formula omitted]-regular, normal subset of a [formula omitted]-regular semigroup, give an alternate characterisation of the maximum idempotent separating congruence in a [formula omitted]-regular semigroup and finally describe the lattice of the idempotent separating congruences in a [formula omitted]-regular semigroup. © 1992, Australian Mathematical Society. All rights reserved.