In this short note, we prove that every twin-free graph on n vertices contains a locating-dominating set of size at most ⌈[Formula presented]n⌉. This improves the earlier bound of ⌊[Formula presented]n⌋ due to Foucaud, Henning, Löwenstein and Sasse from 2016, and makes some progress towards the well-studied locating-dominating conjecture of Garijo, González and Márquez.