The no-cloning principle tells us that nonorthogonal quantum states ca
nnot be cloned, but it does not tell us that orthogonal states can alw
ays be cloned. We suggest a situation where the cloning transformation
s an restricted, leading to a novel type of no-cloning principle. In t
he case of a composite system made of two subsystems: if the subsystem
s 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 o
f quantum cryptography.