  We find several missing one-loop-order contributions in previous
considerations about secondary gravitational waves induced at nonlinear order
in cosmological perturbations. We consider a consistent perturbative expansion
to third-order in cosmological perturbations, including higher-order
interactions and iterative solutions ignored in the previous literature. Tensor
fluctuations induced by the source with two scalar and one tensor perturbations
are correlated with the first-order tensor fluctuation and thus give a
one-loop-order correction to the tensor power spectrum. The missing loop
correction is \textit{scale-invariant} and \textit{negative} in the superhorion
region, which secondarily reduces the initial primordial tensor power spectrum
prior to the horizon re-entry. Such an IR behavior is very different from the
auto-spectrum of second-order induced tensor modes discussed in the previous
literature and can be important for the actual gravitational wave measurements.
For a sharp peak of scalar fluctuations with $A_\zeta=10^{-2}$ at
$k_*=10^{5}h/{\rm Mpc}$ motivated by the LIGO/Virgo events, we show that the
tensor power spectrum at the cosmic microwave background scale reduces by at
most 35%. Hence, the polarization B-mode might not be seen because of the
reduction of the original tensor spectrum due to the secondary effect of
primordial black hole formation.
