China's yuan bounced slightly against a slightly weaker U.S. dollar on Tuesday, stepping off 5 1/2-year lows hit the previous day amid cautious trade as global financial markets struggled to shake off the Brexit shock.

The yuan opened at 6.6512 per dollar in early trade, up from Monday's close of 6.6585 — the lowest close since December 2010. By 0148 GMT, the yuan was at 6.6480. The dollar index edged down 0.3 percent.

Prior to the market open, the People's Bank of China fixed its midpoint at 6.6528, its lowest level since December 2010 and 0.2 percent weaker than the previous fix of 6.6375.

Globally, financial markets continued to be gripped by anxiety after Britain's stunning vote to exit the European Union last week, with the British pound still languishing near its lowest in more than 30 years early on Tuesday.