<p>This paper is a contribution to the topic of ordinal sums of semigroups in the sense of A. H. Clifford and it discusses the basic structure of idempotent pseudo-uninorms on bounded lattices. On bounded lattices, where all points are comparable with a neutral element, a further characterization of idempotent uninorms is shown and idempotent pseudo-uninorms are shown to be decomposable via Clifford’s ordinal sum into semigroups, where the corresponding semigroup operation is either the projection to one of the coordinates or it coincides with the meet or the join with respect to the given lattice order.</p>