The invention relates to a precious-metal recovery method, specifically relates to a method of recovering platinum/rhodium from insoluble residue of dualistic royal water for solving problems of the existing platinum/rhodium recovering method that the process flow is lengthy and complicated, operational process is dangerous, the isolation effect is bad, and the like. The method comprises steps of preprocessing the insoluble residue of royal water by using barium superoxide, oxidizing the platinum and rhodium thereof, dissolving the oxidized platinum and rhodium in hydrochloric acid; using ammonium chloride to deposit platinum after being converted to a sodium type, adding hydrazine hydrate for recovering the spongy platinum, complexing by adding sodium nitrite into the filter liquor after platinum deposition, depositing rhodium by using ammonium chloride, adding hydrochloric acid for dissolving and sodium type conversion, eliminating base metal in the liquid by using ion exchange resin, finally using hydrazine hydrate and hydrogen gas flame for recovering rhodium powder. The method is a precious-metal-resource secondary recovery utilization and purification method, and has advantages of simple technique, short purification period, convenient operations, high coefficient of recovery, little discharging of waste gas and waste matter, and environment protection, and the like.