Consider a benzenoid system with fixed bonds and the subgraph obtained by deleting fixed double bonds together with their end vertices and fixed single bonds without their end vertices. It has often been observed for particular benzenoid systems, and conjectured (or stated) that, in general, such a subgraph has at least two components, and that each component is also a benzenoid system and is normal. But there are no rigorous proofs for that. The aim of this paper is to present mathematical proofs of those two facts. It is also shown that if a benzenoid system has a single hexagon as one of its normal components then it has at least three normal components.