<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <?Pub Dtl=""?>A new efficient technique for computing the Green's functions inside rectangular waveguides is presented. After a summary of the classical approaches and their difficulties, a new strategy is proposed, based on the decomposition of the main spectral series into simpler terms. Although the resulting series present better convergence rate, several acceleration techniques are combined to further improve the efficiency. Several results are presented to demonstrate the improvements in convergence rates obtained using the new decomposition. </para>