There are many methods and approaches to calculate the scattering of electromagnetic waves by non-spherical particles. The most popular method among them appears to be the T-matrix. This method is universal as in principle it can be applied to scatterers of any shape, however one considers mainly axisymmetric scatterers, as otherwise calculations become too computational time-consuming. A new T-matrix-like-method to solve the problem of scattering of a plane electromagnetic wave by dielectric particles with the axial symmetry was suggested by Farafonov, Il'in and Henning (see J. Quant. Spectr. & Rad. Transf. vol.63, p.205, 1999). We develop a similar approach for perfectly conducting axisymmetric bodies and discuss its applicability range.