  General expressions for the double-lepton polarizations in the (B -> K l^+
l^-) decay are obtained, using model independent effective Hamiltonian,
including all possible interactions. Correlations between the averaged
double-lepton polarization asymmetries and the branching ratio, as well as, the
averaged single-lepton polarization asymmetry are studied. It is observed that,
study of the double-lepton polarization asymmetries can serve as a good test
for establishing new physics beyond the Standard Model.
