  Omega Centauri is the most well studied Globular Cluster because of its
numerous puzzling features. Intensive spectroscopic follow-up observing
campaigns targeting stars at different positions on the color-magnitude diagram
promises to clarify some of these peculiarities. To able to target cluster
members reliably during spectroscopic surveys and both spatial and radial
distributions in the cluster outskirts without including field stars, a high
quality proper-motion catalog of omega Cen and membership probability
determination are required. The only available wide field proper-motion catalog
of omega Cen is derived from photographic plates, and only for stars brighter
than B~16. Using ESO archive data, we create a new, CCD-based, proper-motion
catalog for this cluster, extending to B~20. We used the high precision
astrometric software developed specifically for data acquired by<EMAIL_ADDRESS>telescope and presented in the first paper of this series. We achieved a good
cluster-field separation with a temporal base-line of only four years. We
corrected our photometry for sky-concentration effects. We provide calibrated
photometry for UBVRI wide-band data plus narrow-band filter data centered on
H_alpha for almost 360 000 stars. We can confirm that the omega Cen metal-poor
and the metal-rich components have the same proper motion, and demonstrate that
the metal-intermediate component in addition exhibits the same mean motion as
the other RGB stars. We provided membership probability determination for
published omega Cen variable star catalogs. Our catalog extends the
proper-motion measurements to fainter than the cluster turn-off luminosity, and
covers a wide area (~33'x33') around the center of omega Cen. Our catalog is
now electronically available to the astronomical community.
