A complete phase diagram was determined for the system water, decane, isostearic acid, and triethanolamine using optical microscopy and low-angle X-ray diffraction. The system contained two isotropic liquids in the form of an isostearic acid/decane solution with dissolved triethanolamine as well as a water/triethanolamine solution with dissolved isostearic acid and decane. Two lyotropic liquid crystals were found, one of lamellar structure and one consisting of a hexagonal array of close-packed cylinders. Of the two-phase spaces connecting the two liquids with the lamellar liquid crystal one was initiated toward the aqueous solution/decane line, while the other on emanated from the decane/isostearic acid/triethanolamine plane.