  We introduce a novel parafermionic theory for which the conformal dimension
of the basic parafermion is 3(1-1/k)/2, with k even. The structure constants
and the central charges are obtained from mode-type associativity calculations.
The spectrum of the completely reducible representations is also determined.
The primary fields turns out to be labeled by two positive integers instead of
a single one for the usual parafermionic models. The simplest singular vectors
are also displayed. It is argued that these models are equivalent to the
non-unitary minimal W_k(k+1,k+3) models. More generally, we expect all
W_k(k+1,k+2 beta) models to be identified with generalized parafermionic models
whose lowest dimensional parafermion has dimension beta(1-1/k).
