We combine the results of CDF and DO searches for the rare decays B_s to mu+ mu- and B_d to mu+ mu-. The experiments use 364 pb-1 and 300 pb-1 of data respectively. The limits on the branching ratios are obtained by normalizing the estimated sensitivity to the decay B+ to J/psi K+, taking into account the fragmentation ratios f_u/f_s(d). The combined results exclude branching ratios of BR(B_s to mu+ mu-) > 1.5x10-7 and BR(B_d to mu+ mu- > 4.0x10-8 at 95% confidence level. These are the most stringent limits on these decays at the present time.
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