  We show how to produce antideuteron, antihelium, and other antinuclei in
large fractions from the decays of a new particle $\phi$ that carries baryon
number. Close to threshold, the production of nuclear bound states is preferred
over the decay into individual nucleons, effectively decoupling antinuclei and
antiproton fluxes and allowing the former to dominate, in clear contrast to
antimatter production via coalescence. $\phi$ can either form dark matter
itself or be produced by it, and can give rise to a potentially testable amount
of antinuclei.
