We have developed a new formulation of the coupled-wave method (CWM) to handle aperiodic lamellar structures, and it will be referred to as the aperiodic coupled-wave method (ACWM). The space is still divided into three regions, but the fields are written by use of their Fourier integrals instead of the Fourier series. In the modulated region the relative permittivity is represented by its Fourier transform, and then a set of integro-differential equations is derived. Discretizing the last system leads to a set of ordinary differential equations that is reduced to an eigenvalue problem, as is usually done in the CWM. To assess the method, we compare our results with three independent formalisms: the Rayleigh perturbation method for small samples, the volume integral method, and the finite-element method.