We study a class of Abelian quantum Hall (QH) states which are topologically unstable ( T unstable). We find that the T-unstable QH states can have a phase transition on the edge which causes a binding between electrons and reduces the number of gapless edge branches. After the binding transition, the single-electron tunneling into the edge gains a finite energy gap, and only certain multielectron cotunneling (such as three-electron cotunneling for ν = 9/5 edges) can be gapless. We point out that the binding transition can also be viewed as an edge reconstruction transition.
