A forming process of tailor blanks having local thickening for the deep drawing of square cups was developed to improve the drawability. A sheet having uniform thickness is bent into a hat shape of two inclined portions, and then is compressed with a flat die under restraint of both edges to thicken the two inclined portions. The bending and compression are repeated after a right-angled rotation of the sheet for thickening in the perpendicular direction. The thickness of the rectangular ring portion equivalent to the bottom corner of the square cup is increased, particularly the thickening at the four edges of the rectangular ring undergoing large decrease in wall thickness in the deep drawing of square cups becomes double. The degree of thickening can be adjusted by controlling the punch stroke in the bending. By using the tailor blanks having local thickening, not only the decrease in wall thickness at the bottom corner of the square cup was prevented, but also the limiting drawing height of the cup without fracture was increased to 28.3 mm, whereas that for the uniform blank was 21.3 mm.