This paper is a kind of continuation of the paper by G. Deschrijver ‘Uninorms which are neither conjunctive nor disjunctive in interval-valued fuzzy set theory’, which was published in Information Sciences in 2013. In that paper he constructed uninorms whose neutral element is arbitrary of the type \({\mathbf e}=(e,e)\) and annihilator, \(\mathbf {a}\), is arbitrary point that is incomparable with \(\mathbf {e}\). In the present paper we intend to show what are all possibilities of the position of the pair \((\mathbf {e},\mathbf {a})\).