Butterfield Bank’s share price fell by 3.8 percent in New Year’s Eve trading on the Bermuda Stock Exchange, sending the local stock market lower on the last trading day of 2010.Butterfield fell five cents to close on $1.25, as 1,800 of the bank’s shares changed hands on Friday.No other domestic board issues traded. The Royal Gazette / BSX Index closed down 23.92 points, or two percent, lower at 1,142.49.BSX trading turnover topped $30,000, composed of BD$2,250 for 1,800 shares and US$28,467.50 for 2,950 shares.The BSX Insurance Index of the Island’s leading international insurance companies fell three points, or 0.29 percent, to 1,027.