The strong coupling between secondary and tertiary structure formation in protein folding is neglected in most structure prediction methods. In this work we investigate the extent to which nonlocal interactions in predicted tertiary structures can be used to improve secondary structure prediction. The architecture of a neural network for secondary structure prediction that utilizes multiple sequence alignments was extended to accept low-resolution nonlocal tertiary structure information as an additional input. By using this modified network, together with tertiary structure information from native structures, the Q3-prediction accuracy is increased by 7-10% on average and by up to 35% in individual cases for independent test data. By using tertiary structure information from models generated with the ROSETTA de novo tertiary structure prediction method, the Q3-prediction accuracy is improved by 4-5% on average for small and medium-sized single-domain proteins. Analysis of proteins with particularly large improvements in secondary structure prediction using tertiary structure information provides insight into the feedback from tertiary to secondary structure.