The Swiss bank last reviewed its list of external law firms in 2005, and the current appointments will last for a further two years.
The process was led by Europe, Middle East and Africa general counsel Andrew Williams.
On the last UBS panel review the bank asked firms to disclose statistics about diversity for the first time.
Firms were told to provide details of diversity policies, as well as relevant statistics, in their written submissions.
UBS saw its balance book badly damaged by the credit crunch and was forced to write down about $37bn (£18.5bn) in the aftermath of the banking crisis.
The bank declined to comment on the latest panel review.