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The conventional finite-element method (FEM) deteriorates the convergence characteristic of the incomplete Cholesky conjugate gradient (ICCG) method in magnetic field analyses when there are extreme thin elements in meshes. The convergence characteristic is drastically improved by a proposed method, where common unknown variables are simply added to near parallel edges. The number of unknowns is increased, but the rank of the equation is not changed and the condition of the matrix becomes better. The method for thin elements presented in the paper is an application of ldquosingularity decomposition techniquerdquo (SDT) in common with the - formulation and the implicit correction multigrid method.