The sensitivity to the invisible decay of the mass eigen state $\nu_3$ in the presence of
Earth matter effects is studied. Only the charged current interactions of atmospheric $\nu_\mu$ and
$\bar{\nu}_\mu$ for 500 kTon year exposure of a future magnetised iron detector at INO are analysed. The analysis
with observed muon energy in the range would give a constraint of $\tau_3/m_3>1.51\times10^{-10}$ s/eV
at 90\% CL with this exposure. Here $\tau_3$ is the lifetime and $m_3$ is the mass of $\nu_3$, when it
is the heaviest. The effect of decay on the precision measurement of $\sin^2\theta_{23}$ and
$|\Delta{m^2_{32}}|$ and neutrino mass hierarchy are also studied. Since the presence of decay affects
the oscillation amplitude rather than its phase, it is seen that the precision on $\sin^2\theta_{23}$
worsens whereas that on $|\Delta{m^2_{32}}|$ is not much affected. Sensitivity to hierarchy also
worsens slightly in the presence of the invisible decay of $\nu_3$.