Monitoring flows at routers for flow analysis or deep packet inspection requires the monitors to update monitored flow information at the transmission line rate and needs to use highspeed memory such as SRAM. Therefore, it is difficult to measure all flows, and the monitors need to limit the monitoring target to a part of the flows. However, if monitoring targets are randomly selected, an identical flow will be monitored at multiple routers on its route, or a flow will not be monitored at any routers on its route. To maximize the number of flows monitored in the entire network, the monitors are required to select the monitoring targets while maintaining a balanced load among the monitors. In this paper, we propose an autonomous load balancing method where monitors exchange monitor load information with only adjacent monitors.