  We focus on the non-locality concerning local copying and local
discrimination, especially for a set of orthogonal maximally entangled states
in prime dimensional systems, as a study of non-locality of a set of states. As
a result, for such a set, we completely characterize deterministic local
copiability and show that local copying is more difficult than local
discrimination. From these result, we can conclude that lack algebraic symmetry
causes extra non-locality of a set.
