This paper is concerned with an inverse matrix factorization based on Cholesky factorization for ill-conditioned matrices. Recently, Ogita and Oishi derived an iterative algorithm to calculate an accurate approximate inverse of the exact Cholesky factor for such matrices. In this paper, a modified version of the algorithm is proposed. It is explained that the proposed algorithm gives more accurate results than the original one by a numerical analysis. Numerical evidence is also shown.