We present a new method to accelerate the HITS algorithm by exploiting hyperlink structure of the web graph. The proposed algorithm extends the idea of authority and hub scores from HITS by introducing two diagonal matrices which contain constants that act as weights to make authority pages more authoritative and hub pages more hubby. This method works because in the web graph good authorities are pointed to by good hubs and good hubs point to good authorities. Consequently, these pages will collect their scores faster under the proposed algorithm than under the standard HITS. We show that the authority and hub vectors of the proposed algorithm exist but are not necessarily be unique, and then give a treatment to ensure the uniqueness property of the vectors. The experimental results show that the proposed algorithm can improve HITS computations, especially for back button datasets.