In this correspondence, the singular point (SP) problem peculiar to an integer orthonormal transform is discussed, and compatibility of the integer transform with the corresponding real-valued transform is improved. To avoid the SP problem, we introduce two-point permutations of order and sign of signals. Since it satisfies the commutative law, it becomes possible to reduce computational cost to find the best combination of the permutations which minimizes errors due to rounding of signals inside the integer transform.