A surface which carries a material which is infected with prions is cleaned with an alkaline cleaning solution to remove as much proteinaceous material as possible from the surface. The cleaning agent is an alkaline cleaning agent which attacks prions remaining on the surface and which attacks prions removed from the surface during the cleaning step. After the cleaning solution is drained, a solution of surfactants, buffers, and heavy metal free corrosion inhibitors is circulated over the surface at 50null-60null C. The surfactants disperse and unclump the prion-contaminated material. A strong oxidant, preferably peracetic acid, is added to the solution to bring the peracetic acid concentration to 1,000-2,500 ppm. The peracetic acid or other strong oxidant attacks the prions, particularly the unclumped prion strands, deactivating the prions. After rinsing and drying, the surface may be wrapped in a microbe impermeable barrier and subjected to terminal sterilization, such as steam autoclaving.