  The recent reported Glashow resonance (GR) event shows a promising prospect
in the test of the Lorentz violation (LV) by the high-energy astrophysical
neutrinos (HANs) around the resonant energy. However, since the production
source and the energy spectra of HANs are uncertain at present, moderate LV
effects may be concealed at the TeV energy-scale. In this paper, we propose the
LV Hamiltonian of a special texture which can lead to the decoupling of
$\nu_{\mu}$ ($\bar{\nu}_{\mu}$). On the base of the decoupling, a noticeable
damping of the GR event rate is shown for the HANs from the source dominated by
$\bar{\nu}_{\mu}$, irrespective of the energy spectra of the HANs at Earth.
Accordingly, the observation of GR events may bring stringent constraints on
the LV and the production mechanism of HANs.
