  We introduce a new wave phenomenon, which can be observed in continuum and
discrete systems, where a trapped mode exists under certain conditions, namely,
the anti-localization of non-stationary linear waves. This is zeroing of the
non-localized propagating component of the wave-field in a neighbourhood of an
inclusion. In other words, it is a tendency for non-stationary waves to
propagate avoiding a neighbourhood of an inclusion. The anti-localization is
caused by a destructive interference of the harmonics involved into the
representation of the solution in the form of a Fourier integral. The
anti-localization is associated with the waves from the pass-band, whereas the
localization related with a trapped mode is due to poles inside the stop-band.
In the framework of a simple illustrative problem considered in the paper, we
have demonstrated that the anti-localization exists for all cases excepting the
boundary of the domain in the parameter space where the wave localization
occurs. Thus, the anti-localization can be observed in the absence of the
localization as well as together with the localization. We also investigate the
influence of the anti-localization on the wave-field in whole.
