  In this letter we compute some elementary properties of the Fedosov star
product of Weyl type, such as symmetry and order of differentiation. Moreover,
we define the notion of a star product of Wick type on every K\"ahler manifold
by a straight forward generalization of the corresponding star product in
$\mathbb C^n$: the corresponding sequence of bidifferential operators
differentiates its first argument in holomorphic directions and its second
argument in antiholomorphic directions. By a Fedosov type procedure we give an
existence proof of such star products for any K\"ahler manifold.
