A temperature variational ESR measurement was carried out for a phthalocyanine assembly system which is composed of two lutetium phthalocyanine dimer radical. The assembly system, to which we refer as "(2+2) tetramer", is a biradical and shows a typical ESR signal of triplet state in random orientation in solution. The intensity change of the signal corresponding to the triplet state over the range from 8.5K to 60K was undetectablly small. For the determination of the energy levels of the triplet and singlet state, we calculated the exchange interaction term as well as the zero field splitting constant using semiempirical MO of the dimer.