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Mobile WiMAX is an emerging broadband wireless communication technology. The IEEE 802.16e standard for Mobile WiMAX, the enhanced version of the IEEE 802.16 standard with mobility support, defines that the implementation of hard handover is mandatory. However, the long interruption of hard handover is horrible for delay and packet loss sensitive real-time applications such as IPTV and VoIP. To solve this problem without many changes to 802.16e equipments, we propose some improvements at various stages of the handover, including the principle for selection of target base station depending on the type of traffic connection managed by subscriber station. Simulation results prove that the scheme accelerates handover process and make Real-time downlink data transmission interruption so brief that users will not perceive the interruption.