  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 \Delta 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 |\Delta
m_{41}^2| \gg |\Delta 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 \nu_\tau detectors at the short and long
baselines, and we do not find a substantial improvement of the sensitivities.
