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A novel learning algorithm, the Recurrent Neural Network Constrained Optimization Method (RENNCOM) is suggested in this paper, for training block-diagonal recurrent neural networks. The training task is formulated as a constrained optimization problem, whose objective is twofold: 1) minimization of an error measure, leading to successful approximation of the input/output mapping and 2) optimization of an additional functional, the payoff function, which aims at ensuring network stability throughout the learning process. Having assured the network and training stability conditions, the payoff function is switched to an alternative form with the scope to accelerate learning. Simulation results on a benchmark identification problem demonstrate that, compared to other learning schemes with stabilizing attributes, the RENNCOM algorithm has enhanced qualities, including, improved speed of convergence, accuracy and robustness. The proposed algorithm is also applied to the problem of the analysis of lung sounds. Particularly, a filter based on block-diagonal recurrent neural networks is developed, trained with the RENNCOM method. Extensive experimental results are given and performance comparisons with a series of other models are conducted, underlining the effectiveness of the proposed filter.