No cloning of orthogonal states in composite systems

The no-cloning principle tells us that nonorthogonal quantum states cannot be cloned, but it does not tell us that orthogonal states can always be cloned. We suggest a situation where the cloning transformations an restricted, leading to a novel type of no-cloning principle. In the case of a composite system made of two subsystems: if the subsystems are only available one after the other then there are various cases when orthogonal states cannot be cloned. Surprising examples are given, which give a radically better insight regarding the basic concepts of quantum cryptography.