  The notion of the Wick star-product is covariantly introduced for a general
symplectic manifold equipped with two transverse polarisations. Along the lines
of Fedosov method, the explicit procedure is given to construct the Wick
symbols on the manifold. The cohomological obstruction is identified to the
equivalence between the Wick star-product and the Fedosov one. In particular in
the K\"ahler case, the Wick star-product is shown to be equivalent the Weyl
one, iff the manifold is a Calabi-Yau one.
