[en] We propose a modification of the classification of exact Bethe Ansatz eigenstates for a finite Heisenberg magnetic ring in terms of rigged string configurations of Kerov, Kirillov and Reshetikhin. The key change consists in replacing riggings by appropriate quasimomenta resulting from translational symmetry of the ring, and yields an interpretation of strings as objects which are kinematically independent each of another. The size of admissible and forbidden part of the Brillouin zone for strings of the length l is pointed out.