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Supporting mobility is both promising and challenging feature of the emerging IEEE 802.16e wireless networks, commonly known as WiMAX. Although the IEEE has released an amendment to the original IEEE 802.16 standard in which mobility and handover are added as basic capabilities, the amended standard (IEEE 802.16e) defines only a frame work without providing specific methods or algorithm for handover that can be deployed in mobile stations to enable them to switch seamlessly from one base station to another. In this paper, we propose a new handover algorithm for deployment in 802.11e- capable stations. The algorithm takes into consideration the main important aspects of IEEE 802.16 operation such as ranging, authorization, and registration. A special capability built into the proposed algorithm is service-flows awareness, i.e. the algorithm tries to minimize the the time spent in handover based on the service flows running at the mobile station. Analysis of the proposed algorithm shows that handover time can be reduced by several folds by taking advantage of different capabilities provided by the standard.