The purpose of this article is to investigate the presence of a cointegrating relationship between the prices of the two most important crude oil price benchmarks, which are West Texas Intermediate and Brent, for June 1987-July 2021. We use the periodogram-based methodology. Our finding suggests a global long-run relationship between two major crude oil prices for the 1987:06-2010:03 period until the Deepwater Horizon oil spill took place at the Macondo Field, located in the Gulf of Mexico. After this accident, the relationship breaks down. We also find statistically significant closely 12-month common periodicities in both series for the pre-oil spill accident. We conclude that the cointegrating relationship between the two oil prices maintained up to 2010:03. This finding provides a practical implication that these two crude oil prices cannot be used for hedging purposes after this date.