  The no-cloning principle tells us that non-orthogonal 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 are 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.
