We study the problem of exchanging messages within a fixed group of k nodes, in an n-node multi-hop radio network, also known as the problem of Multipoint-to-Multipoint (M2M) multicasting. While the radio network topology is known to all nodes, we assume that the participating nodes are not aware of each other's positions. We give a new fully distributed deterministic algorithm for the M2M multicasting problem, and analyze its complexity. We show that if the maximum distance between any two out of fc participants is d then this local information exchange problem can be solved in time O(d log2 n + k log3 n). Hence our algorithm is linear in the size of the subnetwork induced by the participating nodes and only polylogarithmic in the size of the entire radio network.