A vibration-rotation-tunneling (VRT) spectrum of (H2O)(4) has been recorded near 2.04 THz (67.9 cm(-1)). The band origin of this Delta K = 0 symmetric rotor spectrum is shifted by 0.1 cm(-1) to the blue of that of a (D2O)(4) band reported previously [Science, 1996, 271, 59]. Similar to that spectrum, each transition in the (H2O)(4) spectrum exhibits a regular doublet splitting. The (D2O)(4) and (H2O)(4) doublet spacings, 5.6 and 2260 MHz, respectively, are constant as a function of rotation, indicative of degenerate tunneling splittings. They have been rationalized in terms of a concerted flipping motion of the H atoms that do not participate in hydrogen bonding in the S-4 equlibrium structure, analogous to ammonia inversion. Both bands have been assigned to the lowest A(g)-->B-g intermolecular vibration in the molecular symmetry group C-4h(M). Additional K = 2 splittings, which increase nonlinearly with increasing J, were found in both D2O and H2O tetramer spectra. Evidence for the bifurcation tunneling motion observed in the water trimer VRT data, but not in evidence for (D2O)(4), was found in the (H2O)(4) spectrum in the form of broadened lines probably containing unresolved bifurcation tunneling splittings. Structural estimates from the data indicate that the interoxygen separations in both (D2O)(4) and (H2O)(4) are consistent with an exponential contraction in that parameter as a function of increasing cluster size.