On an overlay network where a number of nodes work autonomously in a decentralized way, the efficiency of broadcasts has a significant impact on the performance of distributed systems built on the network. While a broadcast method using a spanning tree produces a small number of messages, the routing path lengths are prone to be relatively large. Moreover, when multiple nodes can be source nodes, inefficient broadcasts often occur because the efficient tree topology differs for each node. To address this problem, we propose a novel protocol in which a source node selects an efficient tree from multiple spanning trees when broadcasting. Our method shortens routing paths while maintaining a small number of messages. We examined path lengths and the number of messages for broadcasts on various topologies. As a result, especially for a random graph, our proposed method shortened path lengths by approximately 28% compared with a method using a spanning tree, with almost the same number of messages.