It is known by a result of Mendes and Sampaio that the Lipschitz normal embedding of a subanalytic germ is fully characterized by the Lipschitz normal embedding of its link. In this note, we show that the result still holds for definable germs in any o-minimal structure on (ℝ, +, .). We give an example showing that for homomorphisms between MD-homologies induced by the identity map, being isomorphic is not enough to ensure that the given germ is Lipschitz normally embedded. This is a negative answer to the question asked by Bobadilla et al. in their paper about moderately discontinuous homology. K E Y W O R D S definable sets, Lipschitz normal embeddings, MD-homology, o-minimal structures M S C ( 2 0 2 0 ) 14B05, 32C05 INTRODUCTIONGiven a connected definable set 𝑋 ⊂ ℝ 𝑛 , one can equip 𝑋 with two natural metrics: the outer metric (𝑑 𝑜𝑢𝑡 ) induced by the Euclidean metric of the ambient space ℝ 𝑛 and the inner metric (𝑑 𝑖𝑛𝑛 ), where the distance between two points in 𝑋 is defined as the infimum of the lengths of rectifiable curves in 𝑋 connecting these points. We call 𝑋 Lipschitz normally embedded (or LNE for brevity) if these two metrics are equivalent, that is, there is a constant 𝐶 > 0 such that ∀𝑥, 𝑦 ∈ 𝑋, 𝑑 inn (𝑥, 𝑦) ≤ 𝐶𝑑 out (𝑥, 𝑦).Any such 𝐶 is referred to as a LNE constant for 𝑋. We say that 𝑋 is LNE at a point 𝑥 0 ∈ 𝑋 (or the germ (𝑋, 𝑥 0 ) is LNE) if there is a neighborhood 𝑈 of 𝑥 0 in ℝ 𝑛 such that 𝑋 ∩ 𝑈 is LNE. It is worth noticing that, in the o-minimal setting, the definitions of connected and path connected set are equivalent, and every continuous definable curve connecting two points is rectifiable, that is, it has finite length. The notion of LNE first appeared in a paper of Birbrair and Mostowski [5], it has since been an active research area and many interesting results were proved, see, for example, [1-5, 9-13, 19-21]. Recently, Mendes and Sampaio [18] gave a nice criterion for the germ of a subanalytic set to be LNE based on the LNE condition on the link. Namely, they prove that 2958