Summary: Faber polynomials are used to study the properties of univalent functions, and also provide a valuable tool for approximating analytic functions on domains by polynomials. In this note, we give a recurrence relation for Faber polynomials with respect to univalent functions of the class \(\Sigma\), and from this a new computable formula for the Faber coefficients of analytic functions is obtained. Under certain circumstances, it is simpler than those available in the literature.