We discuss the effects of one additional sterile neutrino at the Neutrino Factory. Compared to earlier analyses, which have been motivated by LSND results, we do not impose any constraint on the additional mass squared splitting. This means that the additional mass eigenstate could, with small mixings, be located among the known ones, as it is suggested by the recent analysis of cosmological data. We use a self-consistent framework at the Neutrino Factory without any constraints on the new parameters. We demonstrate for a combined short and long baseline setup that near detectors can provide the expected sensitivity at the LSND-motivated ��m_{41}^2-range, while some sensitivity can also be obtained in the region of the atmospheric mass splitting from the long baselines. We point out that limits on such very light sterile neutrinos may also be obtained from a re-analysis of atmospheric and solar neutrino oscillation data, as well as from supernova neutrino observations. In the second part of the analysis, we compare our sensitivity with the existing literature using additional assumptions, such as |��m_{41}^2| \gg |��m_{31}^2| leading to averaging of the fast oscillations in the far detectors. We demonstrate that while the Neutrino Factory has excellent sensitivity compared to existing studies using similar assumptions, one has to be very careful interpreting these results for a combined short and long baseline setup where oscillations could occur in the near detectors. We also test the impact of additional ��_��detectors at the short and long baselines, and we do not find a substantial improvement of the sensitivities.

23 pages with 8 figures and 1 table included. More references added