A method for continuously casting a slab using a curved type or vertical bending type continuous casting machine, the method comprising: the step of cooling the slab just beneath a mold in a secondary cooling zone, the slab being withdrawn from the mold, the step further comprising: a first water cooling step, a first recuperation step that follows the first water cooling step, a second water cooling step that follows the first recuperation step, and a second recuperation step that follows the second water cooling step, wherein the first water cooling step is a step of cooling the slab of which a surface temperature is no less than 1000°C, by supplying cooling water to wide surfaces of the slab, including that only a surface temperature of a corner part is below Ar 3 point, and a surface temperature of a portion of the slab other than the corner part is kept no less than Ar 3 point, the corner part being a region within 20 mm from an apex and edges of the slab, the first recuperation step is a step of recuperating the slab including that the surface temperature of all the slab including the corner part is no less than the Ar 3 point, the second water cooing step is a step of cooling the slab of which the surface temperature is the Ar 3 point to 900°C, by supplying the cooling water to the wide surfaces of the slab, including that the surface temperature of all the slab including the corner part is below the Ar 3 point, and the second recuperation step is a step of recuperating the slab including that the surface temperature of the corner part is kept below the Ar 3 point, and the surface temperature of the portion of the slab other than the corner part is no less than the Ar 3 point. the step of cooling the slab just beneath a mold in a secondary cooling zone, the slab being withdrawn from the mold, the step further comprising: a first water cooling step, a first recuperation step that follows the first water cooling step, a second water cooling step that follows the first recuperation step, and a second recuperation step that follows the second water cooling step, wherein the first water cooling step is a step of cooling the slab of which a surface temperature is no less than 1000°C, by supplying cooling water to wide surfaces of the slab, including that only a surface temperature of a corner part is below Ar 3 point, and a surface temperature of a portion of the slab other than the corner part is kept no less than Ar 3 point, the corner part being a region within 20 mm from an apex and edges of the slab, the first recuperation step is a step of recuperating the slab including that the surface temperature of all the slab including the corner part is no less than the Ar 3 point, the second water cooing step is a step of cooling the slab of which the surface temperature is the Ar 3 point to 900°C, by supplying the cooling water to the wide surfaces of the slab, including that the surface temperature of all the slab including the corner part is below the Ar 3 point, and the second recuperation step is a step of recuperating the slab including that the surface temperature of the corner part is kept below the Ar 3 point, and the surface temperature of the portion of the slab other than the corner part is no less than the Ar 3 point.