In this paper we study non-standard neutrino interactions as an example of physics beyond the standard model using atmospheric neutrino data collected during the Super-Kamiokande I(1996-2001) and II(2003-2005) periods. We focus on flavor-changing-neutral-currents (FCNC), which allow neutrino flavor transitions via neutral current interactions, and effects which violate lepton non-universality (NU) and give rise to different neutral-current interaction-amplitudes for different neutrino flavors. We obtain a limit on the FCNC coupling parameter, varepsilon_{mu tau}, |varepsilon_{mu tau}|<1.1 x 10^{-2} at 90%C.L. and various constraints on other FCNC parameters as a function of the NU coupling, varepsilon_{e e}. We find no evidence of non-standard neutrino interactions in the Super-Kamiokande atmospheric data.
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