  The theory of vectors and spinors in 9+1 dimensional spacetime is introduced
in a completely octonionic formalism based on an octonionic representation of
the Clifford algebra $\Cl(9,1)$. The general solution of the classical
equations of motion of the CBS superparticle is given to all orders of the
Grassmann hierarchy. A spinor and a vector are combined into a $3 \times 3$
Grassmann, octonionic, Jordan matrix in order to construct a superspace
variable to describe the superparticle. The combined Lorentz and supersymmetry
transformations of the fermionic and bosonic variables are expressed in terms
of Jordan products.
