A liner segment (10) for a rotary ore grinding mill (1) is disclosed. The mill has a horizontal mill axis (25), and an interior having a cylindrical liner (6) with a frusto-conical end (8) from which ground ore slurry exits the mill. Each segment includes a part collar (12) which protrudes inwardly into the interior. The collar has a first generally cylindrical surface (13) co-axial with the mill axis and a second flange surface forming a substantially annular flange (14) of greater radius than the cylindrical surface, surrounding an interior end of the cylindrical surface, and being connected to the cylindrical surface. Each segment has a vane (21) extending radially outwardly of the first cylindrical surface and projecting into the interior. The vane impedes the exit from said mill of unground ore particles and grinding media, and permits the exit of the slurry. A method is also disclosed.