  The NESSiE Collaboration has been setup to undertake a conclusive experiment
to clarify the {\em muon--neutrino disappearance} measurements at short
baselines in order to put severe constraints to models with more than the
three--standard neutrinos. To this aim the current FNAL--Booster neutrino beam
for a Short--Baseline experiment was carefully evaluated by considering the use
of magnetic spectrometers at two sites, near and far ones. The detector
locations were studied, together with the achievable performances of two
OPERA--like spectrometers. The study was constrained by the availability of
existing hardware and a time--schedule compatible with the undergoing project
of multi--site Liquid--Argon detectors at FNAL.
  The settled physics case and the kind of proposed experiment on the Booster
neutrino beam would definitively clarify the existing tension between the
$\nu_{\mu}$ disappearance and the $\nu_e$ appearance/disappearance at the eV
mass scale. In the context of neutrino oscillations the measurement of
$\nu_{\mu}$ disappearance is a robust and fast approach to either reject or
discover new neutrino states at the eV mass scale. We discuss an experimental
program able to extend by more than one order of magnitude (for neutrino
disappearance) and by almost one order of magnitude (for antineutrino
disappearance) the present range of sensitivity for the mixing angle between
standard and sterile neutrinos. These extensions are larger than those achieved
in any other proposal presented so far.
