We have derived a new form of the integral equation formulation of the measured equation of invariance (IE-MEI). The new formulation clarifies the existence of a relationship between scattered electric and magnetic fields at consecutive nodes in the IE-MEI and indicates that the relationship in a problem for a perfect electric conductor (PEC) holds for a problem with arbitrary materials. In a scattering problem of a two-dimensional cylinder with an impedance boundary condition (IBC), every matrix in the IE-MEI is a band-like sparse matrix. That is, the solution process in the IE-MEI with an IBC is the same as that for a PEC. Therefore the IE-MEI with an IBC has the same merits of the IE-MEI for a PEC: The more efficient computation can be achieved with the smaller memory than those of the method of moments (MOM). The IE-MEI with an IBC is validated by numerical examples for a circular cylinder and a square cylinder by comparison with a combined field MOM that satisfies exact boundary conditions. Numerical examples show that the IE-MEI with an IBC is applicable to the case where the generalized skin depth is less than half the width of a scatterer. ¿ 1999 American Geophysical Union