AbstractIn this paper we discuss and expand the direct‐iterative method proposed originally by Wilson.1 First we introduce several simple numerical examples to illustrate the basic idea of this method before we proceed to prove the convergence of the direct‐iterative method. We then discuss the methods for selecting the transformative matrix (Q) to be used in transforming an ill‐conditioned matrix into a well‐conditioned matrix in the direct‐iterative method. There are two methods used to choose the matrix Q, namely the rigid body movement method and the imaginary element method. From examples 1‐3 we can see that the imaginary element mesh is optional, and the finite element mesh is not necessary. The imaginary element method is a generalization of the mesh refinement method development in Reference 3. Because instead of local rotation angle we only choose displacements of nodes to represent rigid body movement, the rigid body movement method is an improvement of the method in Reference 2. The advantage of these two methods is that, in order to obtain well‐conditioned matrices, only a few changes in the stiffness matrices are required even with general ill‐conditioned stiffness matrices, and then convergency is achieved rapidly under SOR iteration. Finally, the examples for computing each type of the ill‐conditioned matrix in three‐dimensional finite element analysis are presented to demonstrate the effectiveness of the direct‐iterative method in solving the large bandwidth problems.