A new incomplete factorization method is proposed, differing from previous ones by the way in which the diagonal entries of the triangular factors are defined. A comparison is given with the dynamic modified incomplete factorization methods of Axelsson–Barker and Beauwens, and with the relaxed incomplete Cholesky method of Axelsson and Lindskog. Theoretical arguments show that the new method is at least as robust as both previous ones, while numerical experiments made in the discrete PDE context show an effective improvement in many practical circumstances, particularly for anisotropic problems.