In this work, the structure of uninorms not locally internal on the boundary is discussed. We first study a conjunctive uninorm U with neutral element e, where the boundary function U(1, .) of U only has two points of discontinuity and one of them is 0 or e. We partially obtain the structure of the conjunctive uninorm U. Its complete structure, under some additional conditions, is achieved as well. For the structure of a disjunctive uninorm U, whose boundary function U(0, .) only has two points of discontinuity and one of them is 1 or e, we obtain similar results. (C) 2021 Elsevier B.V. All rights reserved.
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