We contemplate a higher-level bipolar abstract argumentation for non-elementary arguments such as: X argues against Ys sincerity with the fact that Y has presented his argument to draw a conclusion C, by omitting other facts which would not have validated C. Argumentation involving such arguments requires us to potentially consider an argument as a coherent block of argumentation, i.e. an argument may itself be an argumentation. In this work, we formulate block argumentation as a specific instance of Dung-style bipolar abstract argumentation with the dual nature of arguments. We consider internal consistency of an argument(ation) under a set of constraints, of graphical (syntactic) and of semantic nature, and formulate acceptability semantics in relation to them. We discover that classical acceptability semantics do not in general hold good with the constraints. In particular, acceptability of unattacked arguments is not always warranted. Further, there may not be a unique minimal member in complete semantics, thus sceptic (grounded) semantics may not be its subset. To retain set-theoretically minimal semantics as a subset of complete semantics, we define semi-grounded semantics. Through comparisons, we show how the concept of block argumentation may further generalise structured argumentation.