We study production of sterile neutrinos in the atmosphere and their detection at Super-Kamiokande. A sterile neutrino in the mass range $1\,{\rm MeV} \lesssim M_N \lesssim 105\,{\rm MeV}$ is produced by muon or pion decay, and decays to an electron-positron pair and an active neutrino. Such a decay of the sterile neutrino leaves two electron-like Cherenkov rings in the detector. We estimate the sterile neutrino flux from the well-established active neutrino fluxes and study the number of the decay events in the detector. The upper bounds for the active-sterile mixings are obtained by comparing the $2e$-like events from the sterile neutrino decays and the observed data by Super-Kamiokande. The upper bound for the muon type mixing $��_��$ is found to be $|��_��|^2 \lesssim 5 \times 10^{-5}$ for $20 \,{\rm MeV} \lesssim M_N \lesssim 80\,{\rm MeV}$, which is significantly loosened compared to the previous estimation. We demonstrate that the opening angle and the total energy of the rings may serve as diagnostic tools to discover the sterile neutrinos in further data accumulation and future upgraded facilities. The directional asymmetry of the events is a sensitive measure of the diminishment of the sterile neutrino flux due to the decays on the way to the detector.

23 pages, 14 figures; a comment on the active-sterile oscillation is added (v2)