Swiss bank UBS AG (UBS: sentiment, chart, options) said it will close the offshore accounts of its U.S. clients, as a probe into alleged tax evasion continues. Customers of the bank have been given the option of transferring their assets into a unit of UBS regulated by the U.S., or simply switching banks. Those clients who don't respond to the bank's request for instructions may simply receive checks.

"UBS is progressing with the closings in an orderly fashion," said spokesman Serge Steiner. The bank is under investigation because U.S. authorities believe that some wealthy UBS clients are taking advantage of Switzerland's highly secretive banking laws to dodge paying taxes.

If any customers are guilty of evading taxes, simply transferring their funds or closing out the accounts may not save them from discovery by the Department of Justice. The moves will create a paper trail through which authorities can track them down. However, a few UBS clients who have preemptively turned themselves in to the Internal Revenue Service have avoided harsh punishment so far.

As midday approaches, the U.S.-traded shares of UBS are up nearly 1% at $15.19.