  The cross sections for producing K$^-$ mesons in nucleon-hyperon elementary
processes are estimated assuming one-pion exchange and using the experimentally
known pion-hyperon cross sections. The results are implemented in a transport
model which is applied to calculation of proton-nucleus collisions. In
significant difference to earlier estimates for heavy-ion collisions the
inclusion of the nucleon-hyperon cross section roughly doubles the K$^-$
production in near-threshold proton-nucleus collisions.
