Cognitive radio (CR) is the most promising solution to spectrum scarcity and spectrum underutilization problems. Most of the research in CR design ignores the cost of channel handover process (CHP) in cognition cycle. However, CHP can be a time consuming process that consists of spectrum sensing, spectrum decision, negotiation through control channel, and adjustment of frequency and modulation settings. Taking all of these steps into account, we deduce that the frequency of CHP is one of the most critical CR design issues. In this sense, initiating the CHP after detecting each primary user (PU) activity can decrease the aggregated spectrum utilization. In this paper, we analyze the trade-off between initiating a CHP to find an idle channel and staying in the current data channel for a while to catch free slots when some PU activity is detected. We propose a novel channel handover strategy (CHS) to balance this trade-off. In this CHS, secondary users (SUs) track only their current data channel and do not need information about the whole spectrum environment to determine whether to start CHP or not. Simulation results show that the proposed CHS can clearly decrease the frequency of handovers and increase the aggregated SU utilization.