Mining frequent itemsets through static Databases has been extensively studied and used and is always considered a highly challenging task. For this reason it is interesting to extend it to data streams field. In the streaming case, the frequent patterns' mining has much more information to track and much greater complexity to manage. Infrequent items can become frequent later on and hence cannot be ignored. The output structure needs to be dynamically incremented to reflect the evolution of itemset frequencies over time. In this paper, we study this problem and specifically the methodology of mining time-sensitive data streams. We tried to improve an existing algorithm by increasing the temporal accuracy and discarding the out-of-date data by adding a new concept called the "Shaking Point". We presented as well some experiments illustrating the time and space required.