  The peculiar velocity function of clusters of galaxies is determined using an
accurate sample of cluster velocities based on Tully-Fisher distances of Sc
galaxies (Giovanelli et al 1995b). In contrast with previous results based on
samples with considerably larger velocity uncertainties, the observed velocity
function does not exhibit a tail of high velocity clusters. The results
indicate a low probability of $\lesssim$\,5\% of finding clusters with
one-dimensional velocities greater than $\sim$ 600 {\kms}. The root-mean-square
one-dimensional cluster velocity is 293$\pm$28 {\kms}. The observed cluster
velocity function is compared with expectations from different cosmological
models. The absence of a high velocity tail in the observed function is most
consistent with a low mass-density ($\Omega \sim$0.3) CDM model, and is
inconsistent at $\gtrsim 3 \sigma$ level with $\Omega$= 1.0 CDM and HDM models.
The root-mean-square one-dimensional cluster velocities in these models
correspond, respectively, to 314, 516, and 632 {\kms} (when convolved with the
observational uncertainties). Comparison with the observed RMS cluster velocity
of 293$\pm$28 {\kms} further supports the low-density CDM model.
