Most algorithms for mining sequential rules focus on generating all sequential rules. These algorithms produce an enormous number of redundant rules, making mining inefficient in intelligent systems. In order to solve this problem, the mining of non-redundant sequential rules was recently introduced. Most algorithms for mining such rules depend on patterns obtained from existing frequent sequence mining algorithms. Several steps are required to organize the data structure of these sequences before rules can be generated. This process requires a great deal of time and memory. The present study proposes a technique for mining non-redundant sequential rules directly from sequence databases. The proposed method uses a dynamic bit vector data structure and adopts a prefix tree in the mining process. In addition, some pruning techniques are used to remove unpromising candidates early in the mining process. Experimental results show the efficiency of the algorithm in terms of runtime and memory usage.