  We study the prospects for the exotic Higgs decay mode $h\to ss\to 4\tau$ at
planned electron-positron colliders in the case where the beyond-the-Standard
Model particle $s$ is too light to decay into $b \bar b$ pairs. We find that
with 5 ab$^{-1}$ of unpolarized collisions at 240 GeV, the branching ratio into
this final state can be constrained to be below $\sim 1.3\times 10^{-4}$ at
95\% CL, depending on the mass of $s$ and the assumed tracking efficiency.
