  It is pointed out that searching for sterile neutrinos at high energy regions
at a future IceCube-like facility has advantages compared with that of reactor
or short baseline accelerator neutrino experiments, in which the size of the
detector and energy resolution make it difficult to gain good sensitivity for a
large mass-squared difference. In this study we show that it is possible to
improve constraints on sterile neutrino mixing $\theta_{14}$ for 1
eV$^2~\lesssim \Delta m_{41}^2\lesssim$ 100 eV$^2$ by looking for a dip in the
shower events at an IceCube-like neutrino telescope whose volume is at least 10
times as large as that of IceCube and duration is 10 years. We also give an
analytic expression for the oscillation probabilities in two cases where the
condition of one mass scale dominance is satisfied.
