It is demonstrated that the composite structure of quarks and leptons can be embedded in the SO(10) model of the strong and electroweak interactions. There appear two entities: two bosonic spinors ξ and ξ′ of SO(4) and a fermionic spinor B of SO(6). All the 16's of fermions can be expressed as ( ξjB α ) and (ξ′j B ∗ α) , where j=1 or 2 and α=0, 1, 2, 3 indicating the color SU(4) indices. Further consideration leads us to find a basic entity, ζ transforming as 5 under SU(5), of which the charge is (+ 1 2 , 0, − 1 6 , − 1 6 ) − 1 6 ) and ξ, ξ′ and B can be constructed from ζ and ζ . Although ξ, ξ′ and B obey the SO(10) gauge group, ζ cannot be controlled by SO(10). Some unknown interactions may govern the behavior of ζ at very high energies, where the unification based on SO(10) with ξ, ξ′ and B is destroyed.