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This paper studies the stability problem of a class of recurrent neural networks (RNNs) with multiple delays. By using an augmented matrix-vector transformation for delays and a novel line integral-type Lyapunov-Krasovskii functional, a less conservative delay-dependent global asymptotical stability criterion is first proposed for RNNs with multiple delays. The obtained stability result is easy to check and improve upon the existing ones. Then, two numerical examples are given to verify the effectiveness of the proposed criterion.