  After a brief discussion of the computational complexity of Clifford
algebras, we present a new basis for even Clifford algebra Cl(2m) that
simplifies greatly the actual calculations and, without resorting to the
conventional matrix isomorphism formulation, obtains the same complexity. In
the last part we apply these results to the Clifford algebra formulation of the
NP-complete problem of the maximum clique of a graph introduced in a previous
paper.
