The method includes exclusively releasing a first corner protection (B) and a second corner protection (C) to rest on the upper face and at a respective corner of a first flank of a stack (A) of tiles and moving the stack (A) of tiles so that the corner protections impact against a first packaging element (F). Downstream of the contact, the first packaging element (F) prevents the corner protections from falling and, thereafter, stabilises them after being folded on the stack (A) of tiles by first folding means (2), during the continuance of the movement. The machine (1) comprises release means (5) which comprise hands and actuators to release corner protections. The hands form couples configured to release the corner protections in time sequence, the hands of each pair releasing a respective corner protection in time phase with one another. The machine (1) comprises positioning means of the packaging elements, folding means for folding them on the stack (A) of tiles and movement means which enable the packaging element to contact the corner protections and the folding means.