Aramex fell as the price of the region's biggest courier company adjusted ahead of an expected cash dividend payment of 5 fils per share.
Aramex's shares fell 1.6 per cent to trade today at Dh1.79 each at 11am Dubai time.
Tamweel, the mortgage finance company complying with Shariah rules, fell for a second consecutive day. Retail investors were disappointed after the company made a $21.5 million provision for litigation, causing first quarter profit to drop 33 per cent.
The Dubai Financial Market General Index fell 0.3 per cent to 1637.22 points.
Property stocks led the declines in Abu Dhabi.
Aldar Properties lost 1.7 per cent to Dh1.11. Sorouh Real Estate lost 1.8 per cent to Dh1.09. RAK Properties slumped 5 per cent to 38 fils. The Abu Dhabi Securities Exchange General Index was little changed at 2511.34 points.
Asian markets were mixed after data from Japan showed the country's trade deficit reached a record of 4.41 trillion yen ($54 billion). Japan's Nikkei 225 Index lost 0.9 per cent to 9578.21 points. Korea's Kospi Index lost 0.7 per cent to 813.34 points. Hong Kong's Hang Seng Index was up 0.3 per cent to 20,856.50 points.
Elsewhere in the region, Kuwait's measure added 0.1 per cent to 6277.00 points. Bahrain's index was little changed at 1154.05 points. Oman's MSM 30 Index added 0.5 per cent to 6039.35 points. Qatar's QE Index was little changed at 8717.09 points.
The Saudi Tadawul was closed for the day.