Processing a join over unbounded input streams requires unbounded memory, since every tuple in one infinite stream must be compared with every tuple in the other. In fact, most join queries over unbounded input streams are restricted to finite memory due to sliding window constraints. So far, non-indexed and indexed stream equijoin algorithms based on sliding windows have been proposed in many literatures. However, none of them takes non-equijoin into consideration. In many cases, non-equijoin queries occur frequently. Hence, it is worth to discuss how to process non-equijoin queries effectively and efficiently. In this paper, we propose an indexed join algorithm for supporting non-equijoin queries. The experimental results show that our indexed non-equijoin techniques are more efficient than those without index.