The election problem in a circle of n processors has been studied either assuming bidrectional message-passing but no global sense of orientation, or assuming a global sense of orientation but unidirectional message-passing. To date, no complexity relationship is known between these two cases except that, in both, the worst-case message complexity is Ω(nlogn). In this paper we continue the investigation of the bidirectional case with no global sense of orientation and present an algorithm which requires in the worst case 1.89n logm + 0(n) messages, where m is the number of processors which independently starts the algorithm; since n≥m, this result improves the previous 2nlog n + 0(n) upper-bound for this case. © 1984, Taylor & Francis Group, LLC. All rights reserved.