  We study the consequences of invisible decay of neutrinos in the context of
the DUNE experiment. We assume that the third mass eigenstate is unstable and
decays to a light sterile neutrino and a scalar or a pseudo-scalar. We consider
DUNE running in 5 years neutrino and 5 years antineutrino mode and a detector
volume of 40 kt. We obtain the bounds on the rest frame life time $\tau_3$
normalized to the mass $m_3$ as $\tau_3/m_3 > 4.50\times 10^{-11}$ s/eV at 90\%
C.L. for a normal hierarchical mass spectrum. We also find that DUNE can
discover neutrino decay for $\tau_3/m_3 > 4.27\times 10^{-11}$ s/eV at 90\%
C.L. In addition, for an unstable $\nu_3$ with an illustrative value of
$\tau_3/m_3$ = $1.2 \times 10^{-11}$ s/eV, the no decay case gets disfavoured
at the $3\sigma$ C.L. At 90\% C.L. the allowed range for this true value is
obtained as $1.71 \times 10^{-11} > \tau_3/m_3 > 9.29\times 10^{-12}$ in units
of s/eV. We also study the correlation between a non-zero $\tau_3/m_3$ and
standard oscillation parameters and find an interesting correlation in the
appearance channel probability with the mixing angle $\theta_{23}$. This alters
the octant sensitvity of DUNE, favorably (unfavorably) for true $\theta_{23}$
in the lower (higher) octant. The effect of a decaying neutrino does not alter
the hierarchy or CP discovery sensitivity of DUNE in a discernible way.
