This article reports a new seasonality in the volatility of Eurofutures contracts as a function of the time left before contract expiry. The fact that futures markets, unlike foreign exchange or equity markets, offer contracts that expire on specific dates, with typically one expiry per quarter for Eurofutures, leads to a new type of volatility seasonality as a function of the time left to expiry for the contract in question. The intraday volatility, averaged over the Eurofutures contracts we studied (Eurodollar, Euromark, and Short Sterling), decreases as a function of the time left to expiry. There is also an unexpected behavior consisting of oscillatory movements in volatility, with peaks every 60 business days, corresponding to rollover activities before each quarterly expiry.