The neutron magnetic moment ..mu../sub n/ has been measured with an improvement of 2 orders of magnitude in experimental accuracy. The separated-oscillatory-field magnetic resonance technique was employed using slow neutrons and protons (in flowing water) in the same magnetic field. We find the ratio of neutron to proton moment to be ..mu../sub n//..mu../sub p/ = -0.684 979 35(17) (0.25 ppm). Expressed in Bohr magnetons ..mu../sub B/ this gives ..mu../sub n//..mu../sub B/ = -1.041 875 64(26) x 10/sup -3/. Expressed in nuclear magnetons ..mu../sub N/, ..mu../sub n//..mu../sub N/ = -1.913 041 84(88).