The present invention comprises an improved method for refining cellulose that produces a highly refined cellulosic material. The method comprises soaking raw material from primarily parenchymal cell wall structures in an aqueous solution which need not contain an agent to modify the fiber (e.g., a mild alkalizing or alkaline agent and/or solution) using reduced temperatures and pressures, and refining the material with a plate refiner so that a waste water stream is reduced in volume. The mass is dried to produce the HRC fiber. The HRC fiber displays a water retention capacity of about 25 to at least about 56 g H2O/g dry HRC and retains moisture under conditions that are ordinarily used to remove moisture from materials. The highly refined fiber product can also provide excellent thickening properties and can be used in a wide variety of materials, including edible materials.