Abstract: By using the formalism ofsecond quantization and irreducible tensor,quasispin angular momentum scalaroperator Z(K),where K=2,…,2j,is constructed from 4 creation-annihilation operators.Theeigenvalues of Z(K) have special ability for classification of coupled states,by angular momentum J and quasispin Q the complete classification can be done only for j≤7/2,but by eigenvalues of Z(K)the complete classification have be donefor j≤15/2.The methods for calculating the eigenvalues of Z(K)are discussed,and the complete classifications for j≤15/2 are presented.