Words whose every k(≥ 3) successive factors of the same length are all different, i.e., kanti-power words are natural extensions of square-free words (every two successive factors of the same length are different). We give a way to verify whether a uniform morphism preserves k-anti-power words, i.e., the image by this morphism of all k-anti-power words are k-anti-power words. A consequence of the existence of such morphisms is the possibility of generating an infinite k-anti-power word.