The maximum planarization problem is to find a spanning planar subgraph having the largest number of edges for a given graph. In this paper, we propose a self-stabilizing algorithm to solve this problem for complete bipartite networks. The proposed algorithm finds the maximum planar subgraph of 2n-4 edges in O(n) rounds, where n is the number of nodes. (C) 2009 Elsevier B.V. All rights reserved.