Successful protein secondary structure prediction is an important step towards modelling protein 3D structure, with several practical applications. Even though in the last four decades several PSSP algorithms have been proposed, we are far from being accurate. The Bidirectional Recurrent Neural Network (BRNN) architecture of Baldi et al. [1] is currently considered as one of the optimal computational neural network type architectures for addressing the problem. In this paper, we implement the same BRNN architecture, but we use a modified training procedure. More specifically, our aim is to identify the effect of the contribution of local versus global information, by varying the length of the segment on which the Recurrent Neural Networks operate for each residue position considered. For training the network, the backpropagation learning algorithm with an online training procedure is used, where the weight updates occur for every amino acid, as opposed to Baldi et al. [1], where the weight updates are applied after the presentation of the entire protein. Our results with a single BRNN are better than Baldi et al. [1] by three percentage points (Q3) and comparable to results of [1] when they use an ensemble of 6 BRNNs. In addition, our results improve even further when sequence-to-structure output is filtered in a post-processing step, with a novel Hidden Markov Model-based approach.