  We obtain new results on the stability of discrete dark solitons bifurcating
from the anti-continuum limit of the discrete nonlinear Schrodinger equation,
following the analysis of our previous paper [Physica D 212, 1-19 (2005)]. We
derive a criterion for stability or instability of dark solitons from the
limiting configuration of the discrete dark soliton and confirm this criterion
numerically. We also develop detailed calculations of the relevant eigenvalues
for a number of prototypical configurations and obtain very good agreement of
asymptotic predictions with the numerical data.
