A non-orientable structure, said Möbius stripe, is proposed for certain types of circular DNA. This structure could account for particular forms, such as dimers, double length molecules, or catenans which are molecules topologically interwomen. On the other hand, it is suggested that a second structure derived from the same principal of non-orientability could have gendered the dynamics of DNA replication at the origin of life: this is hypothesis of archetype Möbius strip.