The association between log-price increments of exchange-traded equities, as measured by their spot correlation estimated from high-frequency data, exhibits a pronounced upward-sloping and almost piecewise linear relationship at the intraday horizon. There is notably lower-on average less positive-correlation in the morning than in the afternoon. We develop a nonparametric testing procedure to detect such variation in a correlation process. The test statistic has a known distribution under the null hypothesis, whereas it diverges under the alternative. We run a Monte Carlo simulation to discover the finite sample properties of the test statistic, which are close to the large sample predictions, even for small sample sizes and realistic levels of diurnal variation. In an application, we implement the test on a high-frequency dataset covering the stock market over an extended period. The test leads to rejection of the null most of the time. This suggests diurnal variation in the correlation process is a nontrivial effect in practice. We show how conditioning information about macroeconomic news and corporate earnings announcements affect the intraday correlation curve.