  We analyze the non-perturbative structure of the strange sea of the nucleon
within a meson cloud picture. In a low $Q^2$ approach in which the nucleon is
viewed as a three valon bound state, we evaluate the probability distribution
of an in-nucleon Kaon-Hyperon pair in terms of splitting functions and
recombination. The resulting kaon and hyperon probability densities are
convoluted with suitable strange distributions inside the meson and baryon in
order to obtain non-perturbative contributions to the strange sea of the
nucleon. We find a structured strange/anti-strange asymmetry, displaying a
clear excess of quarks (anti-quarks) for large (small) momentum fractions
