We present the current status of the BMV experiment. Our apparatus is based on an up-to-date resonant optical cavity coupled to a transverse magnetic field. We detail our data acquisition and analysis procedure which takes into account the symmetry p
roperties of the raw data with respect to the orientation of the magnetic field and the sign of the cavity birefringence. The measurement result of the vacuum magnetic linear birefringence k_mathrm{CM}$ presented in this paper was obtained with about 200 magnetic pulses and a maximum field of 6.5,T, giving a noise floor of about $8 times 10^{-21}$,T$^{-2}$ at $3sigma$ confidence level.
