Edrei and Szego5 [1] have posed the following problem: Giiven the Foiurier coefficients of a function G(x) find the Fourier coe/ftcients of the reciprocal of the function without actually evaluating G(x). They were able to solve this problem in the case that G(x) ?0. Unfortunately this restriction eliiniiiates the interesting case of complex-valued functions such as those which arise in Laurent series. In this note it is shown possible to obtain a solution withoutthe restriction, G(x) > 0. TFhis is achieved by first treating the more general problem of finding the coefficieiits of F(x)/G(x), given the coefficients of F(x) and G(x). Edrei and Szegd confine attentioni to classical Fourier series. Their problem is treated here for arbitrary orthogonal series expansions.2 Let 0j(x), j= 1, 2, , be a sequenlce of bounded orthoniormal functions in some region R of a space S. Thus