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As of 0228 GMT, the main TAIEX index was lower 78.42 points at 8,882.34, after closing down 0.32 percent on Monday.
Most major subindexes fell with electronics down 0.8 percent and construction lower 1.12 percent.
Transportation was the lone standout, rising 0.5 percent.
The Taiwan dollar was up T$0.048 at T$30.454 to the US dollar.