  A study of diff($S^1$) covariant properties of pseudodifferential operator of
integer degree is presented. First, it is shown that the action of diff($S^1$)
defines a hamiltonian flow defined by the second Gelfand-Dickey bracket if and
only if the pseudodifferential operator transforms covariantly. Secondly, the
covariant form of a pseudodifferential operator of degree n not equal to 0, 1,
-1 is constructed by exploiting the inverse of covariant derivative. This, in
particular, implies the existence of primary basis for W_{KP}^{(n)} (n not
equal to 0, 1, -1).
