As a novel application of string junctions, we provide evidence for the
existence of stable non-BPS dyons with magnetic charge greater than 1 in (the
semiclassical regime of) N=2 SU(2) Super-Yang-Mills theory. In addition, we
find a new curve of marginal stability. Moduli space is therefore divided into
four regions, each containing a different stable particle spectrum.Comment: 12 pages LaTex, 5 figures; Added comments in both section 3 and the
conclusions regarding the applicability of the string web picture in the
field theory limi