Abstract: The conventional FEM obtains field distribution simultaneously. Similarity discretization FEM (SDFEM) realizes the thought of stepwise recurrence. The advantage is that the rank of stiffness matrix is retained at a low level. However, probably due to the strict limitation-similarity discretization, the SDFEM could not deal with the boundary value problem when the field region has multiple media or multi-connected domains. A more general method is presented in this paper. There are not many restrictions on the discretization, so it can solve the problem with multiple media or multi-connected domains conveniently. At the same time, the thought of recurrence may be realized and the advantage of the SDFEM are reserved. The SDFEM also can be regarded as a spedal case of this method.