This paper suggests a new algorithm for selecting the input–output (IO) coefficients of a Leontief matrix in order of importance, so providing an analytical method for decomposing an IO matrix. It avoids the choice of arbitrary thresholds for eliminating flows or coefficients, and allows for circular relationships. For this purpose, a simple inverse-important criterion has been chosen, which is consistent with the logic of the Leontief model. A procedure that greatly reduces the computational burden is then devised. This method permits new comparisons of IO structures of different countries or regions, for identifying their different degree of internal integration and their reciprocal influence through the exchange of intermediate goods. An application to an IO model for seven European Community countries for 1980 is then presented.