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This brief investigates the problem of mean square exponential stability of uncertain stochastic delayed neural networks (DNNs) with time-varying delay. A novel Lyapunov functional is introduced with the idea of the discretized Lyapunov-Krasovskii functional (LKF) method. Then, a new delay-dependent mean square exponential stability criterion is derived by applying the free-weighting matrix technique and by equivalently eliminating time-varying delay through the idea of convex combination. Numerical examples illustrate the effectiveness of the proposed method and the improvement over some existing methods.