Semi-flower languages are those of the form $$L^*$$ for some finite maximal prefix code L, or equivalently, those recognizable by a so-called semi-flower automaton, in which all the cycles have a common state $$q_0$$, which happens to be the initial state and the only accepting state.We show that the syntactic complexity of these languages is exactly $$n^n-n!+n$$ (where n stands for the state complexity as usual) and that this bound is reachable with an alphabet of size n.