A method to make pulp adapted for forming a corrugated medium, the method includes: cooking chips in a cooking vessel using a caustic carbonated pulping soda/caustic (SC) cooking liquor injected into the cooking vessel; fiberizing the chips discharged from the cooking vessel to form a pulp, and removing lignin from the pulp or oxidizing lignin in the pulp by injecting oxygen (O2) into the fiberized pulp.