  Cold dark matter haloes are populated by caustics, which are yet to be
resolved in N-body simulations or observed in the Universe. Secondary infall
model provides a paradigm for the study of caustics in "typical" haloes
assuming that they have had no major mergers and have grown only by smooth
accretion. This is a particular characteristic of the smallest dark matter
haloes of about 10^{-5} Mo, which although "atypical" contain no substructures
and could have survived until now with no major mergers. Thus using this model
as the first guidline, we evaluate the neutralino self-annihilation flux for
these haloes. Our results show that caustics could leave a distinct sawteeth
signature on the differential and cumulative fluxes coming from the outer
regions of these haloes. The total annihilation signal from the regions away
from the centre can be boosted by about forty percents.
