Abstract There are three subalgebra chains in Ginocchlo's so ( 8 ) model. The subalgebra so ( 5 ) + su ( 2 ) and so ( 7 ) are maximum subalgebras in so ( 8 ). The subalgebra so ( 6 ) is not this case. We can find a new subalgebra so ( 7 ) between the so ( 8 ) and so ( 6 ). It is useful in the calculation at least.
