To achieve more accurate result and lower computational complexity of range analysis for multiplication in automatic word length optimization, this paper presents a novel refined affine approximation method of multiplication for range analysis in automatic word length optimization, which is named novel affine arithmetic approximation (NAA). In NAA, a new noise term represents the error which is caused by approximation. This error is estimated more accurately without increasing the computational complexity. The computational complexity of NAA is O(M₁), where M₁ denotes the total of the nonzero noise of the two multipliers. In experiments, the accuracy of the range using NAA is 1.47 times of that using trivial range estimation, and the same as that using Chebyshev approximation.