Horizontal curves have been identified as experiencing more crashes than tangent sections on roadways, especially on rural two-lane highways. The first edition of the Highway Safety Manual provides crash modification functions (CM functions) for curves on rural two-lane highways. The CM functions proposed in the manual may suffer from both outdated data and analysis technique. Before-and-after studies are usually the preferred method for estimating the safety effects of treatments. Unfortunately, this method is not feasible for curves. Previous studies have frequently used regression models for developing CM functions for horizontal curves. As recently documented in the literature, some potential problems exist with using regression models to develop crash modification factors. This research utilized a cross-sectional study to develop curvature CM functions. Curves located on Texas rural two-lane undivided highways were divided into a number of bins based on the curve radius. Safety was predicted with the assumption that these curves had been tangents. The observed number of crashes that occurred on the curves was compared with the dummy tangents and for different bins. The results showed that the horizontal curve radius has a significant role in the risk of a crash. From these results, a new CM function was developed. The prediction performance of the Highway Safety Manual CM function was compared with the new CM function in this study and another function that was recently proposed in the literature. It was found that the new CM function documented in this study outperformed both.