Specifically conceived for mattresses with springs (4), the mattress consists of a cylindrical tubular body (1, 1') with a longitudinal cut line (2) in correspondence with one of its lines of symmetry, that connects its two open ends, towards which open a number of wide notches (3, 3'), with an isosceles trapezoid configuration that, together with the longitudinal opening (2) allow the male-female coupling of the corner piece to the springs (4) of the mattress, externally closing the set of springs at the corresponding corner to provide a smooth, continuous surface without any bulges, recesses or deformations.