The authors present a calculation of the Lyapunov exponent for transverse magnon modes in a Heisenberg spin-glass chain with positive and negative exchange interactions, both analytically as a microcanonical average and also numerically in the usual canonical statistical ensemble. In the positive- omega regime they find that the localization length obeys xi ( omega ) varies as omega ^-1 at omega to 0 if p>q, where p, q=1-p are the +1 and -1 spin concentrations, respectively. It is shown that the previously reported xi ( omega ) varies as omega ^-2/3 singularity, related to the anomalous dispersion law omega varies as k^3/2, holds only in the limit of equal concentrations p=q=0.5. The corresponding densities of states diverge as rho ( omega ) varies as omega ^-1/2 and varies as omega ^-1/3 for p>q and p=q, respectively.