  We calculate the full two-loop electroweak matching corrections to the
operator governing the decay B_q --> l^+ l^- in the Standard Model. Their
inclusion removes an electroweak scheme and scale uncertainty of about 7% of
the branching ratio. Using different renormalization schemes of the involved
electroweak parameters, we estimate residual perturbative electroweak and QED
uncertainties to be less than 1% at the level of the branching ratio.
