The method involves aspirating a face (24) of a cheese (20) by an aspiration unit (50) to grip the cheese and remove the cheese from a cheese grate (10a) by raising the cheese. Another face (22) of the cheese is aspirated by another aspiration unit (60), and aspiration of the former face is stopped when or after the latter face is aspirated. Aspiration of the latter face is continued and the cheese is pivoted so as to position the former face near the grate. Aspiration of the latter face is stopped to liberate the cheese such that the cheese rests on the grate via the former face. An independent claim is also included for a device for turning a dairy product i.e. cheese, during production or ripening of the product.