The knowledge discovery algorithms have become ineffective at the abundance of data and the need for fast algorithms or optimizing methods is required. To address this limitation, the objective of this work is to adapt a new method for optimizing the time of association rules extractions from large databases. Indeed, given a relational database (one relation) represented as a set of tuples, also called set of attributes, we transform the original database as a binary table (Bitmap table) containing binary numbers. Then, we use this Bitmap table to construct a data structure called Peano Tree stored as a binary file on which we apply a new algorithm called BF-ARM (extension of the well known Apriori algorithm). Since the database is loaded into a binary file, our proposed algorithm will traverse this file, and the processes of association rules extractions will be based on the file stored on disk. The BF-ARM algorithm is implemented and compared with Apriori, Apriori+ and RS-Rules+ algorithms. The evaluation process is based on three benchmarks (Mushroom, Car Evaluation and Adult). Our preliminary experimental results showed that our algorithm produces association rules with a minimum time compared to other algorithms.