One of the challenges in protein secondary structure prediction is to overcome the cross-validated 80% prediction accuracy barrier. Here, we propose a novel approach to surpass this barrier. Instead of using a single algorithm that relies on a limited data set for training, we combine two complementary methods having different strengths: Fragment Database Mining (FDM) and GOR V. FDM harnesses the availability of the known protein structures in the Protein Data Bank and provides highly accurate secondary structure predictions when sequentially similar structural fragments are identified. In contrast, the GOR V algorithm is based on information theory, Bayesian statistics, and PSI-BLAST multiple sequence alignments to predict the secondary structure of residues inside a sliding window along a protein chain. A combination of these two different methods benefits from the large number of structures in the PDB and significantly improves the secondary structure prediction accuracy, resulting in Q3 ranging from 67.5 to 93.2%, depending on the availability of highly similar fragments in the Protein Data Bank.