  We consider the Ising spin system, which stems out from the corresponding
Multiple-spin exchange (MSE) Hamiltonian, on the special one--dimensional
lattice, diamond-plaquette chain. Using the technique e of transfer-matrix we
obtain the exact expression for system free energy with the aid of which we
obtain the magnetization function. Analyzing magnetization curves for varies
values of temperature and couplin constants we found the magnetization plateaux
at 1/3 and 2/3 of the full moment.
  The corresponding microscopic spin configurations are unknown by virtue of
high frustration.
