Local structures predicted from protein sequences are used extensively in every aspect of modeling and prediction of protein structure and function. For more than 50 years, they have been predicted at a low-resolution coarse-grained level (e.g., three-state secondary structure). Here, we combine a two-state classifier with real-value predictor to predict local structure in continuous representation by backbone torsion angles. The accuracy of the angles predicted by this approach is close to that derived from NMR chemical shifts. Their substitution for predicted secondary structure as restraints for ab initio structure prediction doubles the success rate. This result demonstrates the potential of predicted local structure for fragment-free tertiary-structure prediction. It further implies potentially significant benefits from using predicted real-valued torsion angles as a replacement for or supplement to the secondary-structure prediction tools used almost exclusively in many computational methods ranging from sequence alignment to function prediction.