It is well known that index fund selections are important for the risk hedge of investment in a stock market. The 'selection' means that for 'stock index futures', n companies of all ones in the market are selected. For index fund selections, Orito et al. (6) proposed a method consisting of the following two steps:Step 1 is to select N companies in the market with a heuristic rule based on the coefficient of determination between the return rate of each company in the market and the increasing rate of the stock price index.Step 2 is to construct a group of n companies by applying genetic algorithms to the set of N companies. We note that the rule of Step 1 is not unique. The accuracy of the results using their method depends on the length of time data (price data) in the experiments. The main purpose of this paper is to introduce a more 'effective rule' for Step 1. The rule is based on turnover. The method consisting of Step 1 based on turnover andStep 2 is examined with numerical experiments for the 1st Section of Tokyo Stock Exchange. The results show that with our method, it is possible to construct the more effective index fund than the results of Orito et al. (6) . The accuracy of the results using our method depends little on the length of time data (turnover data). The method especially works well when the increasing rate of the stock price index over a period can be viewed as a linear time series data.