The present work proposes a novel method to treat the cylindrical coordinate singularity which arises when dealing with three-dimensional confined rotating flows. In this work, we have developed a method which consists in discretizing the whole diameter −R ≤ r ≤ R with an even number of radial Gauss-Lobatto nodes. In the azimuthal direction, the overlap in the discretization and especially the use of parity conditions are avoided by introducing a shift equal to Pi/2K (K the number of mesh points in that direction) for Theta > Pi in the Fourier transform. Spectral convergence of the method is illustrated on steady and unsteady analytical solutions. The ability of our numerical method to investigate complex unsteady flows is then illustrated for two rotating flow problems where other reliable experimental or numerical results are available in the literature.