The TAIEX opened at 10,004.65 points which was the first time the index passed the 10,000-point mark in 15 years.
The bellwether Hon Hai Precision Industry Co. and Largan Precision Co. led a drop in technology stocks. But financial stocks rose 0.8 percent and helped prevent the benchmark index from sliding further.
Taiwan shares closed down 16.29 points, or 0.16 percent, at 9,956.83 Tuesday.