The invention relates to a continuous casting installation, for example for steel billet and bloom formats having substantially rectangular or circular cross-section. The invention improves the strand structure in the corner areas, to avoid rhomboidity, cracks and dimensional imperfections of the strand cross-section while achieving a high throughput capacity per strand and reducing investment and running costs. The fillets of the groove curvatures in the die cavity amount to a proportion of the length of the side of the strand cross-section. The degree of curvature 1/R of the groove curvatures decreases in the direction of the strand at least along at least partial length of the entire casting die, thereby achieving gap elimination between the casting shell and the casting die wall and/or a targeted casting shell shaping in the area of the groove curvature. The continuous casting installation, directly downstream of the casting die, may thus be provided with a strand support-free secondary cooling zone or a supporting guide in the secondary cooling zone that is reduced in its supporting width and/or supporting length.