  We study the $\nu_\mu - \nu_s$ oscillation effects in the near detector of
the MINOS experiment. Conceptually, the MINOS search for sterile neutrinos with
mass $\sim 1$ eV realizes an interesting situation of partial decoherence of
the neutrino state at the production. This corresponds to a difference of
energies of the two mass eigenstates that is comparable with or bigger than the
width of the initial state (pion). We show that these effects modify the MINOS
bound on mixing of sterile neutrino for $\Delta m^2_{41} \aprge 0.5$ eV$^2$ and
make the experiment insensitive to oscillations with $\Delta m^2_{41} \gtrsim
15$ eV$^2$. Oscillations with $\Delta m^2_{41} = (1 - 3)$ eV$^2$ could explain
some deficit of events observed in the low energy bins in the near detector and
correspondingly the excess of events in the far detector.
