  The polarization of the CMBR scattered by galaxy clusters in the kinematic
Sunyaev Zeldovich effect depends on the transverse velocity of the cluster.
This polarizing effect is proportional to the transverse velocity squared, and
so weaker that the change in intensity due to the radial motion in the
kinematic effect. The value given by Sunyaev and Zeldovich, and which is
frequently cited, underestimates the polarizing effect by a factor of ten. We
show furthermore that the polarization has a strong frequency dependence. This
means that the polarization should be detectable with the new generation of
CMBR probes, at least for some clusters. Thus this effect offers, almost
uniquely, a method of obtaining the vectorial velocity of clusters.
