A novel integral formulation of the measured equation of invariance method is derived from the reciprocity theorem and implemented for perfectly conducting (PEC) 2-D scattering problems. This formulation uses the electric and magnetic Green's functions of the environment to obtain a matrix equation for the induced surface current with the same number of unknowns as the conventional boundary element-method of moments (BE-MoM) approach. However, the matrix that must be inverted in the new formulation is sparse and circulant, with only three non-zero elements per row. Sample results for two-dimensional TM and TE problems with perfectly conducting scatterers show enormous CPU time and memory savings over the conventional BEM-MoM approach. The new formulation has important advantages over the original finite difference formulation of MEI, but also shares some of its limitations.