Abstract Amino acids evolve at different speeds within protein sequences, because their functional and structural roles are different. However, the position of an amino-acid within the sequence is not known to influence this evolutionary speed. Here we discovered that amino-acid evolve almost twice faster at protein termini than in their centre, hinting at a strong topological bias along the sequence length. We further show that the distribution of functional domains and of solvent-accessible residues in proteins readily explain how functional constrains are weaker at their termini, leading to the observed excess of amino-acid substitutions. Finally, we show that methods inferring sites under positive selection are strongly biased towards protein termini, suggesting that they may confound positive selection with weak negative selection. These results suggest that accounting for positional information should improve evolutionary models.