We compute the rates of semileptonic BA → BBl⁻l⁻ (l = e or μ) hyperon transitions in a model where intermediate states involve loops of baryons and a Majorana neutrino. These rates turn out to be well below present experimental bounds and other theoretical estimates. From the experimental upper limit on the Ξ⁻ → pμ⁻μ⁻ decay, we derive the bound μμ> ≤ 22 TeV for the effective Majorana mass of the muon neutrino. Also, an estimate of background contributions for these decays due to the allowed BA → BBl⁻l⁻ ν⁻ν⁻ decays is provided.