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Abstract In this paper, we improve the concept of Cm $C^{m}$-almost periodicity on periodic time scales. The concept is based on the revised definition of almost periodicity introduced by Wang and Agarwal in 2015. A theorem is derived for the relationship of Cm $C^{m}$-almost periodic functions on R $\mathbb {R}$ and Cm $C^{m}$-almost periodic functions on periodic time scales.