A possible method for obtaining an orthogonal set constituted by eight kind
s of boson operators is proposed. The motivation is to apply the set obtain
ed ill this paper to three algebras for the study of high temperature super
conductivity, i.e., the so(5), the so(4) and the su(2) x su(2) algebras. Th
e basic idea here comes from two recent papers by the present authors, one
considering a possible method for obtaining an orthogonal set constituted b
y four kinds of boson operators and one considering the coupling scheme of
two su(1, 1) spins. The raising and lowering operators for the magnitude of
the su(2) spin coupled to two su(2) spins are introduced, and it is found
that these operators play an essential role in constructing the set.