The author used Put-Call-Futures Parity, Arbitrage-Free, Ex-ante Tests and Ex-post Tests to examine the arbitrage opportunity and market efficiency of the TAIEX index futures (TX) and the TAIEX index options (TXO) in this paper, during the period of December 24th, 2001 to December 31st, 2002. The author first, used daily closing prices to test for the existence of possible arbitrage opportunities. Second, she used ex-ante tests and arbitrage strategy to examine the arbitrage opportunity whether it exists or not with a time lag. Furthermore, The author classified the samples which exist ex-post arbitrage profit into five sub-samples according to call options positions belonging to near-the-money and far-from-the-money, futures positions belonging to positive basis and negative basis, markets belonging to bull markets and bear markets, and different margin requirement. She used ex-post and ex-ante tests to compare the results of over-all markets samples with the sub-samples, then, she also examined the results of included transaction cost or not. The major findings are as follows: 1. Whether taking into transaction cost or not, the TAIEX index futures and the TAIEX index options markets have arbitrage opportunity¡Aand so the markets unefficient. 2. The results of ex-ante tests and the average of arbitrage profit are positive for time to increase. 3. The long arbitrage strategy generates a higher arbitrage profit than the short arbitrage strategy. 4. The investors could proceed arbitrage profit during markets belonging to positive basis and bear market and low margin requirement.