  Starting from the observed distribution of galaxy clusters in redshift space
we use a two--step procedure to recover their distances and peculiar
velocities. After statistically correcting for the unobserved cluster
distribution in the zone of avoidance ($|b|\le 20^{\circ}$) and also for a
smooth absorption at higher $|b|$'s, we use a dynamical iterative algorithm to
recover the real--space cluster positions by minimizing the redshift space
distortions. The whole procedure assumes that clusters trace the mass, that
peculiar velocities are caused by gravity and that linear perturbation theory
applies. The amplitude of the cluster dipole measured in the 3D space turns out
to be $\sim 23\%$ less than that measured in redshift space. In both cases the
dipole direction is aligned with the Cosmic Microwave Background dipole within
$\sim 10^{\circ}$, taking into account the Virgocentric infall component of the
Local Group motion. Observational errors, limitations in the reconstruction
procedure and the intrinsic cosmological variance, which is the dominant source
of uncertainty, render a stringent determination of the $\beta$ parameter whose
central value turns out to be $\beta \approx 0.2$ while its total uncertainty
is $\pm 0.1$. This implies that for a cluster-mass bias parameter of $\sim 5$,
a flat Universe is not excluded, contrary to previous cluster-dipole $z$-space
analysis.
