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We present the X-ray variability properties of the X-ray and TeV brightblazar Mrk 421 with a ~60 ks long XMM-Newton observation performed on November9-10, 2005. The source experienced a pronounced flare, of which the inter-bandtime lags were determined with a very high confidence level. The soft (0.6-0.8keV) X-ray variations lagged the hard (4-10 keV) ones by 1.09 ks, and the softlag increases with increasing difference in the photon energy. Theenergy-dependent soft lags can be well fitted with the difference of theenergy-dependent cooling timescales of the relativistic electron distributionresponsible for the observed X-ray emission, which constrains the magneticfield strength and Doppler factor of the emitting region to beB\delta^(1/3)~1.78 Gauss.

Discovery of a high confidence soft lag from an X-ray flare of Markarian 421