The asymptotic solution of the singular stress around a three dimensional corner between dissimilar materials was analyzed using the H-integral method. However, we could not obtain the accurate scalar parameters of asymptotic solution for some problems. In this study, we investigated what reduced the accuracy of the solution and how to improve the accuracy. The eigen values and eigen vectors of the asymptotic solution was analyzed by the eigenvalue decomposition of the finite element model of a corner. After that we analyzed a target problem using the elastic finite element method, and performed the H-integral to obtain the scalar parameters. We found out that the some integral equations related with the H-integral, which should be zero, were not zero when we obtained inaccurate scalar parameters. The integral values decrease with refining the finite element meshes for the eigenvalue decomposition, and the obtained scalar parameters approached constant values. The eigenvalue decomposition demanded very fine finite element meshes to obtain the accurate values for some problems.