We analyze a covolume method based on the new nonconforming element introduced by Douglas et al. [1]. We show the H-1 optimal order convergence of the scheme for Stokes problem and study the hybrid domain decomposition procedure for this covolume scheme. The numerical experiment shows that the covolume scheme is somewhat better than finite element scheme in the computation of pressure. (C) 2002 Elsevier Science Ltd. All rights reserved.