  We propose a new approach to probe neutral-current non-standard neutrino
interaction parameter $\varepsilon_{\mu\tau}$ using the oscillation dip and
oscillation valley. Using the simulated ratio of upward-going and
downward-going reconstructed muon events at the upcoming ICAL detector, we
demonstrate that the presence of non-zero $\varepsilon_{\mu\tau}$ would result
in the shift in the dip location as well as the bending of the oscillation
valley. Thanks to the charge identification capability of ICAL, the opposite
shifts in the locations of oscillation dips as well as the contrast in the
curvatures of oscillation valleys for $\mu^-$ and $\mu^+$ is used to constrain
$|\varepsilon_{\mu\tau}|$ at 90% C.L. to about 2% using 500 kt$\cdot$yr
exposure. Our procedure incorporates statistical fluctuations, uncertainties in
oscillation parameters, and systematic errors.
