Ab initio calculations are used to demonstrate the existence of a nonvalence temporary anion shape resonance for a model (H2O)(4) cluster system with no net dipole moment. The cluster is composed of two water dimers, the distance between which is varied. Each dimer possesses a weakly bound nonvalence anion state. For large separations of the dimer subunits, there are two bound nonvalence anion states (of A(g) and B-2(u) symmetry) corresponding to the symmetric and asymmetric combinations of the nonvalence anion states of the two dimer subunits. As the separation between the dimer subunits is decreased, the B-2u anion increases in energy and becomes a temporary anion shape resonance. The real part of the resonance energy is determined as a function of the distance between the dimers and is found to increase monotonically from just above threshold to 28 meV for the range of geometries considered. Over this same range of geometries, the resonance half-width varies from 0 to 21 meV. The B-2(u) anion, both when bound and when temporary, has a very diffuse charge distribution. The effective radial potential for the interaction of the excess electron with the cluster has a barrier at large distance arising from the electron-quadrupole interaction in combination with the repulsive angular momentum (l = 1) contribution. This barrier impacts both the resonance energy and its lifetime.