The aim of this paper is to critically review the traditional typology of argument macrostructures, particularly, the dichotomy between linked and convergent structure. We have found an argument structure that does not fall under one of those five traditional categories: basic, serial, divergent, linked and convergent. We show that the new argument structure, which we call the recursive structure, is not rare-earth, but ubiquitous in real argumentation. Then, we propose and justify a new approach to diagramming arguments of the structure. (...) The new argument structure is really new because arguments of the new structure are analyzed and evaluated differently from those of the other structures, especially from hybrid arguments considered in the literature. In light of the new argument structure, we present a hypothesis why assumptions and exceptions of a defeasible argument play different roles in dialectical settings. (shrink)