This paper presents an efficient technique for the analysis of printed circuits with arbitrarily shaped metallizations. This novel technique is based on the MoM/BI-RME method: it consists in the formulation of an electric field integral equation, which is solved by the Method of Moments (MoM) with entire-domain basis functions. The efficiency of the method derives from the use of the Boundary Integral-Resonant Mode Expansion (BI-RME) method in the determination of the basis functions in the case of fully arbitrary metal patches. The novelty of this work is the formulation of the BI-RME method for the determination of a novel set of basis functions, which enhances the capabilities of a CAD tool previously developed. The BI-RME formulation for calculating entire-domain basis functions with all possible combination of electric/magnetic boundaries is reported.