It is a well-known theorem, due to J. Shalika and I. Piatetski-Shapiro, independently, that any non-zero cuspidal automorphic form on GLn(A) is generic, i.e. has a non-zero WhittakerFourier coefficient. Its proof follows from the Fourier expansion of the cuspidal automorphic form in terms of its Whittaker-Fourier coefficients. In this paper, we extend this Fourier expansion to the whole discrete spectrum of the space of all square-integrable automorphic forms of GLn(A) and determine the Fourier coefficients of irreducible non-cuspidal (residual) automorphic representations of GLn(A) in terms of unipotent orbits.