  We study the persistent edge current in the fractional quantum Hall effect.
We give the grand partition functions for edge excitations of hierarchical
states coupled to an Aharanov-Bohm flux and derive the exact formula of the
persistent edge current. For $m$-th hierarchical states with $m>1$, it exhibits
anomalous oscillations in its flux dependence at low temperatures. The current
as a function of flux goes to the sawtooth function with period $\phi_0/m$ in
the zero temperature limit. This phenomenon provides a new evidence for exotic
condensation in the fractional quantum Hall effect. We propose experiments of
measuring the persistent edge current to confirm the existence of the
hierarchy.
