  Sensitivity of the magnetised Iron CALorimeter (ICAL) detector at the
proposed India-based Neutrino Observatory (INO) to invisible decay of the mass
eigenstate $\nu_3$ using atmospheric neutrinos is explored. A full
three-generation analysis including earth matter effects is performed in a
framework with both decay and oscillations. The wide energy range and baselines
offered by atmospheric neutrinos are shown to be excellent for constraining the
$\nu_3$ lifetime. We find that with an exposure of 500 kton-yr the ICAL
atmospheric experiment could constrain the $\nu_3$ lifetime to
$\tau_3/m_3>1.51\times10^{-10}$ s/eV at the 90\% C.L. This is two orders of
magnitude tighter than the bound from MINOS. The effect of invisible decay on
the precision measurement of $\theta_{23}$ and $|\Delta{m^2_{32}}|$ is also
studied.
