  Motivated by recent experimental results, we reconsider the theory of the
edge excitations for the fractional Hall effect at filling factors
$\nu=p/(2np+1)$. We propose to modify the standard $u(1)\otimes su(p)$ edge
theory for this series by introducing twist fields which change the boundary
conditions of the bosonic fields and simulate the effect of fractions of flux
quanta $\phi_0/p$. This has the effect of removing the conserved charges
associated to the neutral modes while keeping the right statistics of the
particles. The Green function of the electron in presence of twists decays at
long distance with an exponent varying continuously with $\nu$.
