A new, simple, and fast method for the solution of electromagnetic scattering problems for perfectly conducting objects of arbitrary shape is presented. The method is based on an equivalent representation of the conducting object in terms of a circular one having a higher order impedance boundary condition on its surface. As a first result, a new universal relation between the higher order surface impedances and the shape of the object is obtained. Then, by taking advantage of this relationship, the scattering problem related to a conducting object is recast as the solution of a matrix equation whose coefficients are determined from the higher order impedances. Numerical simulations show that the method yields to accurate results, and that, it is computationally effective.