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The neocognitron is a hierarchical, multi-layered neural network capable of robust visual pattern recognition. The neocognitron acquires the ability to recognize visual patterns through learning. The winner-kill-loser is a competitive learning rule recently shown to outperform standard winner-take-all learning when used in the neocognitron to perform a character recognition task. In this paper, we improve over the winner-kill-loser rule by introducing an additional threshold to the already existing two thresholds used in the original version. It is shown theoretically, and also by computer simulation, that the use of a triple threshold makes the learning process more stable. In particular, a high recognition rate can be obtained with a smaller network.