Walsh-Hadamard transform (WHT) based multiplierless integer discrete cosine transform (IntDCT) has structural regularity even in short word length lifting coefficients. It, however, cannot apply to image coding without the quantization part because WHT was implemented by only 1 adder operations without the normalization scaling factors. Although we have already presented a normalized integer WHT (IntWHT) as its solution, it also has many adder operations. In this paper, using a two-dimensional (2-D) separable transform of one-dimensional (1-D) normalized WHT is applied to each lifting coefficient, we present a more simplified realization of normalized IntWHT with structural regularity for short word length lifting coefficients. Finally, in lossless-to-lossy image coding, IntDCT based on the proposed IntWHT is validated.