  We compute the rates of semileptonic B_A \to B_Bl^-l^- (l=e or \mu) 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 \Xi^- \to p\mu^-\mu^- decay, we derive the bound <m_{\mu \mu}> < 22 TeV for
the effective Majorana mass of the muon neutrino. Also, an estimate of
background contributions for these decays due to the allowed B_A \to
B_Bl^-l^-\bar{\nu}\bar{\nu} decays are provided.
