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Previously, fast computational methods based on directly thinning the matrix of method of moments (MoM), such as impedance matrix localization (IML), wavelet expansions, and reduced expansion and field testing (REFT), have been introduced. In this paper, we propose a simpler approach to thin the MoM matrix by using the concept of measured equation of invariance (MEI). This approach is referred to as matrix decomposition by MEI (MDMEI). A little effort is required to add the resulting method to any of a variety of MoM programs for solving problems of wire antennas, and conducting object scattering.