Protein secondary structure (PSS) prediction is an important topic in bioinformatics. Our study on a large set of nonhomologous proteins shows that long-range interactions commonly exist and negatively affect PSS prediction. Besides, we also reveal strong correlations between secondary structure (SS) elements. In order to take into account the long-range interactions and SS-SS correlations, we propose a novel prediction system based on a cascaded bidirectional recurrent neural network (BRNN). We compare the cascaded BRNN against two other BRNN architectures, namely, the original BRNN architecture used for speech recognition and Pollastri's BRNN, which was proposed for PSS prediction. Our cascaded BRNN achieves an overall three-state accuracy Q3 of 74.38 percent and reaches a high Segment Overlap (SOV) of 66.0455. It outperforms the original BRNN and Pollastri's BRNN in both Q3 and SOV. Specifically, it improves the SOV score by 4-6 percent.