  We investigate the double Dalitz decays $B_s \to l^+ l^- l'^+ l'^-$ on the
basis of the effective Hamiltonian for the transition $b \bar{s} \to l^+ l^-$,
and universal form factors suggested by QCD. The correlated mass spectrum of
the two lepton pairs in the decay $B_s \to e^+ e^- \mu^+ \mu^-$ is derived in
an efficient way, using a QED result for meson decays mediated by two virtual
photons: $B_s \to \gamma^* \gamma^* \to e^+ e^- \mu^+ \mu^-$. A comment is made
on the correlation between the planes of the two lepton pairs. The conversion
ratios $\rho_{lll'l'}= \frac{\Gamma(B_s \to l^+ l^- l'^+ l'^-)}{\Gamma(B_s \to
\gamma \gamma)}$ are estimated to be $\rho_{eeee}=3 \times 10^{-4},
\rho_{ee\mu\mu}=9 \times 10^{-5} \text{and} \rho_{\mu\mu\mu\mu}=3 \times
10^{-5}$, and are enhanced relative to pure QED by $10-30 %$.
