The goal of the work is to estimate the neuron states of a neutral type network with time-varying delays through available output measurements for the first time. The authors consider the same problem for the same class of systems as in their previous work [Appl. Math. Comput. 203, No. 1, 217–223 (2008; Zbl 1166.34331
)]. Based on Lyapunov methods and the linear matrix inequality, a novel criterion for the existence of the proposed state estimator of the network is given. This criterion differs from that one derived in [loc. cit.], however, it is proved by the technique analogous to that in the mentioned work.