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Self-monitoring is a simple and effective mechanism for surveilling wireless sensor networks, especially to cope against faulty or compromised nodes. A node v can monitor the communication over a link e if both end-nodes of e are neighbors of v . Finding a set of monitoring nodes satisfying all monitoring constraints is called the edge-monitoring problem . The minimum edge-monitoring problem is known to be NP-complete. In this paper, we present a novel self-stabilizing algorithm for computing a minimal edge-monitoring set under the unfair distributed scheduler. For sparse networks the time complexity of this new algorithm is much lower than the currently best known algorithm. [ABSTRACT FROM AUTHOR]