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Vertical handover is one of the key technologies to support seamless connectivity across multiple wireless communication systems and guarantee quality of service (QoS) for the applications therein. This paper proposes an opportunistic vertical handover scheme for a voice over Internet Protocol (VoIP) connection that makes use of the on-off characteristics of voice traffic by aligning the mutual silence period of the two parties engaged in conversation with the service disruption time that occurs during the vertical handover procedure. From the six-state Brady model, we derive a simplified two-state Markov model in which the characteristics of both the talk-spurt period and the mutual silence period are obtained. We then analyze the performance of the proposed scheme with respect to the handover execution time and the packet loss time. The analysis and simulation results show that the proposed scheme significantly decreases the VoIP packet loss time, whereas the total time required for the vertical handover procedure increases but remains within a tolerable time limit.