We investigate a polarization state fixer that produces light with an arbitrary desired polarization state and constant power from an arbitrary elliptically polarized input light whose principal polarization axis fluctuates randomly. An example of such a device composed of a quarter-wave plate and a polarizer is proposed, and its characteristics at wavelengths of 633 nm and 1550 nm are demonstrated. We conclude that we cannot obtain a passive device that produces fixed-axis, linearly polarized light with a constant power level from an elliptically polarized light with a varying elliptical parameter.