  A new renormalization group treatment is proposed for the critical exponents
of an m-fold Lifshitz point. The anisotropic cases (m not equal 8) are
described by two independent fixed points associated to two independent
momentum flow along the quadratic and quartic directions, respectively. The
isotropic case is described separately. In that case, the fixed point is due to
renormalization group transformations along the quartic directions. The new
scaling laws are derived for both cases and generalize the ones previously
reported.
