We previously introduced a simple and fast method for computing the scattered field when a TM wave is incident on an arbitrary-shaped multilayer cylindrical object. Here, we propose a modification of this method for the TE illumination case. According to this approach, the magnetic field at each layer is expressed as a series of cylindrical functions with unknown coefficients. These coefficients are determined through the solution of a linear system of equations that is obtained by first imposing the boundary conditions, then expressing cylindrical functions as Fourier series on each boundary, and using the orthogonality of complex exponentials. Numerical simulations show that the proposed modification for the TE case is also an efficient alternative numerical technique.