Chemical shifts of backbone atoms in proteins are exquisitely sensitive to local conformation, and homologous proteins show quite similar patterns of secondary chemical shifts. The inverse of this relation is used to search a database for triplets of adjacent residues with secondary chemical shifts and sequence similarity which provide the best match to the query triplet of interest. The database contains 13C alpha, 13C beta, 13C', 1H alpha and 15N chemical shifts for 20 proteins for which a high resolution X-ray structure is available. The computer program TALOS was developed to search this database for strings of residues with chemical shift and residue type homology. The relative importance of the weighting factors attached to the secondary chemical shifts of the five types of resonances relative to that of sequence similarity was optimized empirically. TALOS yields the 10 triplets which have the closest similarity in secondary chemical shift and amino acid sequence to those of the query sequence. If the central residues in these 10 triplets exhibit similar phi and psi backbone angles, their averages can reliably be used as angular restraints for the protein whose structure is being studied. Tests carried out for proteins of known structure indicate that the root-mean-square difference (rmsd) between the output of TALOS and the X-ray derived backbone angles is about 15 degrees. Approximately 3% of the predictions made by TALOS are found to be in error.