In this article we present a new technique for the modal analysis of a coaxial conductor with misaligned inner rod. The value of this method lies in the fact that, being based on linear techniques, it is possible to achieve the cutoff frequencies of the propagating modes without losing precision when the order of the modes increases. The differences in the results, obtained using 225 and 1600 basis functions, is quite negligible. Moreover, the procedure is completely analytical up to the evaluation of projection integrals, and the numerical part is restricted only to the matrix inversion. Therefore the run time needed is very low. This method was implemented in Fortran software written on this purpose by the authors. Numerical results are presented, keeping into account the computational time and complexity, and finally showing good agreement with other results already present in literature.