  We propose a new method for finding discrete eigenvalues for the direct
Zakharov-Shabat problem, based on moving in the complex plane along the
argument jumps of the function $a(\zeta)$, the localization of which does not
require great accuracy. It allows to find all discrete eigenvalues taking into
account their multiplicity faster than matrix methods and contour integrals.
The method shows significant advantage over other methods when calculating a
large discrete spectrum, both in speed and accuracy.
