  The uninorms with continuous underlying t-norm and t-conorm are characterized
via an extended ordinal sum construction. Using the results of [18], where each
uninorm with continuous underlying operations was characterized by properties
of its set of discontinuity points, it is shown that each such a uninorm can be
decomposed into an extended ordinal sum of representable uninorms, continuous
Archimedean t-norms, continuous Archimedean t-conorms and internal uninorms.
