The efficiency and relationship between future and spot index prices has been investigated in literature by using different approaches. In this paper, the efficiency and relationship between the log future prices and the log spot prices is investigated for each contract based on cointegration model with a time trend. A new pairs trading strategy for stock prices cointegrated with time trend is proposed in this paper. Formulas used to evaluate the trading strategy are derived and the necessary conditions for making profit out of selected pairs of assets are discussed. S and P 500 future contracts prices of Mar98, Jun98 and Sep98 as well as their corresponding spot index prices are considered in this paper. Our empirical studies show that the strategy proposed in this paper works very well and produces very significant high return for those selected pairs. The average return per trade for all periods and all those pairs are above 10% .