The sensitivity to the invisible decay of the mass eigenstate ν3 in the presence of Earth matter effects is studied. Only the charged current interactions of atmospheric νµ and νµ 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 τ3/m3 > 1.51×10−10 s/eV at 90% CL with this exposure. Here τ3 is the lifetime and m3 is the mass of ν3, when it is the heaviest. The effect of decay on the precision measurement of sin2 θ23 and |∆m232| 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 sin2 θ23 worsens whereas that on |∆m232| is not much affected. Sensitivity to hierarchy also worsens slightly in the presence of the invisible decay of ν3 © Copyright owned by the author(s) under the terms of the Creative Commons.