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Starting from Sumatra mega-earthquake on December 26, 2004, M=9.1, the intensity of strongest earthquakes in the world was increased dramatically. The data of low-frequency seismic noise from global and some regional broadband seismic networks are available starting from 1997. We can estimate daily median values of some non-linear statistics of seismic noise from all operable stations of these networks. Such estimates show that seismic noise properties have explicit trends. In particular wavelet-based multiscale entropy, index of linear predictability and wavelet-based smoothness index of seismic noise are increasing whereas singularity spectrum support width and spectral exponent are decreasing. At the same time coherence of daily median seismic noise properties from different parts of networks is increasing. These facts are interpreted as increasing of global seismic danger. We can try to connect such trends of the seismic noise with time series of the Earth's rotation irregularity (LOD - length of day) which has been freely available since 1962. Since 1997, this series contains a statistically significant high-frequency component with periods from 2 to 300 days, which is associated with the transition to high-precision measurements using space geodesy. Evaluation of the properties of the LOD series in a sliding time window of 1 year length identified a significant anomaly of increased entropy of the high-frequency component of the LOD time series in 2000. A comparison of the anomalies of the averaged properties of seismic noise on global broadband seismic networks and on network in Japan allows us to propose the hypothesis that the irregularity of the Earth's rotation is reflected in the synchronization of the properties of seismic noise and can be a trigger for the intensification of the strongest earthquakes since the end of 2004.