  We study the primordial tensor perturbation produced from the double
inflationary scenario with an intermediate break stage. Because of the
transitions, the power spectrum deviates from the vacuum one and there will
appear oscillatory behavior. In the case of a scalar-type curvature
perturbation, it is known that the amplitude of these oscillations may be
enhanced to result in the power spectrum larger than the one for the vacuum
case. One might expect the similar enhancement for the tensor perturbation as
well. Unfortunately, it is found that when the equation of state (EOS)
parameter $w=p/\rho$ of the break stage is a constant with $w>-1/3$, the
amplitude of oscillations is never large enough to enhance the power spectrum.
On the contrary, the power spectrum is found to be suppressed even on those
scales that leave the horizon at the first inflationary stage and remain
superhorizon throughout the entire stage. We identify the cause of this
suppression with the correction terms in additional to the leading order
constant solution on superhorizon scales. We argue that our result is general
in the sense that any intermediate break stage during inflation cannot yield an
enhancement of the tensor spectrum as long as the Hubble expansion rate is
non-increasing in time.
