As a novel application of string junctions, we construct stable non-BPS sta
tes on a 3-brane probe in the 7-brane background associated with N = 2 SU(2
) Super-Yang-Mills theory. These states introduce a second curve of margina
l stability, across which some of them decay. Moduli space is therefore div
ided into four regions, each containing a different stable particle spectru
m.