I reexamine the inverted-U relationship between competition and innovation (modeled and tested by Aghion et al. (2005)) by using data from publicly traded manufacturing firms in the United States. I control for the possible endogeneity of competition by using a trade-weighted average of industry exchange rates as an instrument. I find a mildly negative relationship between competition (as measured by the inverse of markups) and innovation (as measured by citation-weighted patents). The negative relationship is robust to many alternative assumptions and specifications. To reconcile the mildly negative relationship in the U.S. data with the inverted-U relationship that Aghion et al. (2005) find in the U.K. data, I modify their theoretical model and show that the modified model can explain both negative and inverted-U relationships. The key theoretical assumption is that the U.K. manufacturing industries are technologically more neck-and-neck than their counterparts in the United States. I find support for this assumption in the data. The different empirical results between the two countries may also arise because of differences in data and samples.