A generalized effective spin-Hamiltonian HSG describing the EPR of transition group ions in crystal is proposed on the basis of group theory. In this method, HSG is considered strictly by the space-time symmetry. In the first order perturbation, the irreducible spin tensors TLM (L=0,1,…, 2S) describe completely the EPR of paramagnetic ions with ground state having (2S + 1) energy levels. Irreducible tensors in several point-group symmetries are presented for convenience of obtaining HSG explicitly. Such a HSG is equivalent to the Koster-Statz matrix.
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