  The lepton polarization asymmetry in the B\to\ell^{+}\ell^{-} decay, when one
of the leptons is polarized, is investigated using the most general form of the
effective Hamiltonian. The sensitivity of the asymmetry to the new Wilson
coefficients is studied.Moreover, correlations between the lepton polarization
asymmetry and the branching ratio is studied. It is observed that, there are
not exist such regions of new Wilson coefficients, which the value of branching
ratio coincides with SM result while the lepton polarization does not, i.e new
physics effects can be established by studying lepton polarization only.
