The wireless sensor network (WSN) is a technology that senses environmental information and provides appropriate services to users. There are diverse application areas for WSNs such as disaster prevention, military, and facility management. Despite the many prospective applications, WSN s are vulnerable to various malicious attacks. In false report attacks, a malicious attacker steals a few sensor nodes and obtains security materials such as authentication keys from the nodes. The attacker then injects false event reports to the network through the captured nodes. The injected false reports confuse users or deplete the limited energy of the nodes in the network. Many filtering schemes have been proposed to detect and remove false reports. In the statistical en route filtering (SEF) scheme, each node shares authentication keys selected from a global key pool. Due to the limited memory, each node is able to store only a small portion of the global key pool. Therefore, the routing paths of the event reports significantly affect the filtering (i.e., detecting) probability of false reports. In this paper, we propose a method to determine the routing paths of event reports both hop by hop and on demand at each node. In this method, each node chooses the next node on the path from the event source to the sink node based on the key indexes of its neighbor nodes. Experiments show that the proposed method is far more energy efficient than the SEF when the false traffic ratio (FTR) is ≥ 50% in the network.