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Global warming is expected to change the regime of extreme precipitation. Physical laws translate increasing atmospheric heat into increasing atmospheric water content that drives precipitation changes. Within the literature, general agreement is that extreme precipitation is changing, yet different assessment methods, data sets, and study periods may result in different patterns and rates of change. Here we perform a global analysis of 8,730 daily precipitation records focusing on the 1964-2013 period when the global warming accelerates. We introduce a novel analysis of the N largest extremes in records having N complete years within the study period. Based on these extremes, which represent more accurately heavy precipitation than annual maxima, we form time series of their annual frequency and mean annual magnitude. The analysis offers new insights and reveals (1) global and zonal increasing trends in the frequency of extremes that are highly unlikely under the assumption of stationarity and (2) magnitude changes that are not as evident. Frequency changes reveal a coherent spatial pattern with increasing trends being detected in large parts of Eurasia, North Australia, and the Midwestern United States. Globally, over the last decade of the studied period we find 7% more extreme events than the expected number. Finally, we report that changes in magnitude are not in general correlated with changes in frequency.