The thickness variation during sheet deep drawing process has an impact on the quality of the final product and can lead to local material fractures. To minimize this phenomenon caused by varying degrees of stretching in different areas of the sheet, various methods can be employed. This research paper introduces a novel technique for metal sheet deep drawing, specifically designed for parts with complex geometric shapes that exhibit significant variations in deformation levels across different areas. The objective of this method is to enhance the quality of the deep drawing process by reducing thickness variations in the final part. In this proposed approach, the vertical movement of the punch is accomplished through two vertical rotational movements. This increases the flexibility of the deformation process, ensuring that the active tools elements occupy the most advantageous positions determined by the material flow in the die. As a result, the material's deformability is improved, allowing for a higher degree of deformation. Additionally, this new method offers a relatively simple design and kinematics solutions for the press and eliminates the need for lengthy assembly-disassembly times.