NMR chemical shifts in proteins depend strongly on local structure. The program TALOS establishes an empirical relation between ¹³C, ¹⁵N and ¹H chemical shifts and backbone torsion angles ϕ and ψ (Cornilescu et al. J Biomol NMR 13 289–302, 1999). Extension of the original 20-protein database to 200 proteins increased the fraction of residues for which backbone angles could be predicted from 65 to 74%, while reducing the error rate from 3 to 2.5%. Addition of a two-layer neural network filter to the database fragment selection process forms the basis for a new program, TALOS+, which further enhances the prediction rate to 88.5%, without increasing the error rate. Excluding the 2.5% of residues for which TALOS+ makes predictions that strongly differ from those observed in the crystalline state, the accuracy of predicted ϕ and ψ angles, equals ±13°. Large discrepancies between predictions and crystal structures are primarily limited to loop regions, and for the few cases where multiple X-ray structures are available such residues are often found in different states in the different structures. The TALOS+ output includes predictions for individual residues with missing chemical shifts, and the neural network component of the program also predicts secondary structure with good accuracy.