A method of producing a unitary pipe having a combination of square and circular cross sections comprising the steps of securely clamping a workpiece or a pipe having a square cross section to a workpiece grip of a lathe machine; spinning the securely clamped workpiece according to a predetermined spinning speed by operating the lathe machine; heating up a predetermined portion of the workpiece with a heating torch; extinguishing the heating torch once the required maximum temperature is reached; pressing a roller having a flat rim against the heated portion of the workpiece to gradually transform its square cross section into a circular cross section; and pressing the transformed portion with a roller having a round rim when the workpiece is at a predetermined lower temperature to produce a rounded common spot of the square cross section and the transformed circular cross section.