A recapitulation of the development of anti symmetry theory is given in the introduction. "Black-white" ornamental motifs occurring in ornamental art are classified by using symmetry criteria, according to the corresponding antisymmetry groups. Antisymmetry groups of rosettes, friezes and ornaments are illustrated by examples from Neolithic and ancient ornamental art. The principle of modularity is used in order to explain possible methods of construction of certain ornaments, and to reconstruct some of them only from their parts preserved in archaeological material.