A novel mechanism for dephasing in dielectric glasses is considered. T
he mechanism is due to the delocalized collective excitations arising
in the ensemble of the interacting two-level systems. The spectral dif
fusion induced by these excitations gives rise to the phonon-independe
nt transverse relaxation. The mechanism results in the linear temperat
ure dependence of the dephasing rate and becomes predominant at ultral
ow temperatures. A qualitative agreement with the experimental data is
found.