  We present the X-ray variability properties of the X-ray and TeV bright
blazar Mrk 421 with a ~60 ks long XMM-Newton observation performed on November
9-10, 2005. The source experienced a pronounced flare, of which the inter-band
time lags were determined with a very high confidence level. The soft (0.6-0.8
keV) X-ray variations lagged the hard (4-10 keV) ones by 1.09 ks, and the soft
lag increases with increasing difference in the photon energy. The
energy-dependent soft lags can be well fitted with the difference of the
energy-dependent cooling timescales of the relativistic electron distribution
responsible for the observed X-ray emission, which constrains the magnetic
field strength and Doppler factor of the emitting region to be
B\delta^(1/3)~1.78 Gauss.
