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To obtain the good flatness of hot-rolled stainless-steel strips, high-precision shape control has always been the focus of research. In hot rolling, the quadratic wave (centre buckle and edge wave) can usually be controlled effectively. However, the quarter buckle of the strip is still a challenge to solve. In this paper, a prediction model of roll deflection and material flow is established to study the change rule and control technology of the quarter buckle. The effects of the process parameters on the quarter buckle are analysed quantitatively. The process parameters affect the quarter buckle and the quadratic wave simultaneously. This coupling makes the control of the quarter buckle difficult. The distribution of lateral temperature and the quartic crown of the strip have less effect on the quadratic wave but have a great effect on the quarter buckle. Finally, a new technology for work roll contour is developed to improve the quarter buckle. Through industrial application, the model and the new contour are proved to be effective.