Without assuming the monotonicity and differentiability of activation functions and the symmetry of interconnections, Wang and Zou [Wang L, Zou X. Harmless delays in Cohen-Grossberg neural networks, Physica D 2002;170:162-73] established three sufficient conditions for the global asymptotic stability of a unique equilibrium of the Cohen-Grossberg neural network with multiple discrete time delays. These criteria are all independent of the magnitudes of the delays, and so the time delays under these conditions are harmless. More interestingly, their numerical results indicate that the first two of these criteria actually ensure the global exponential stability of the unique equilibrium. In this paper, we will provide rigorous proofs of these numerical observations. Some further numerical simulations are given to illustrate the theoretical results.