A multichannel photoelectric Zeeman analyzer has been used to investigate the magnetic nature of the spotted UV Ceti flare stars. Magnetic observations were obtained on a sample of 19 program objects, of which 5 were currently spotted dKe-dMe stars, 7 were normal dK-dM stars, 7 were UV Ceti flare stars, and 1 was a possible post-T Tauri star. Contrary to most previously published observations and theoretical expectations, no magnetic fields were detected on any of these objects from either the absorption lines or the H-alpha emission line down to an observational uncertainty level of 100-160 gauss (standard deviation).