  A construction of $W$-symmetries is given only in terms of the nonlocal
fields (parafermions ${\ps}_{\al}$), which take values on the homogeneous space
$G/U(1)^r$, where $G$ is a simply connected compact Lie group manifold (its
accompanying Lie algebra ${\cal G}$ is a simple one of rank $r$). Only certain
restriction of the root set of Lie algebra on which the parafermionic fields
take values are satisfied, then a consistent and non-trivial extension of the
stress momentum tensor may exist. For arbitrary simple-laced algebras, i.e. the
$A-D-E$ cases, a more detailed discussion is given. The OPE of spin three
primary field are calculated, in which a primary field with spin four is
emerging.
