It is becoming general that the contour of part is defined with free-form curves for abrasive waterjet cutting. In this paper, the effect of the traverse speed on cut surface quality is discussed. After that, the free-form Pythagorean Hodographs (PH) curve is defined and its main characteristics are discussed. A new CNC interpolator capable of driving the nozzle along the PH curves at the feedrate adaptable of the curvature of the contour is presented. The taper shape or jet lag can be minimized with it through the variation of the traverse speed. Experimental data indicate that a decrease of about 58 per cent in kerf taper angle can be obtained under a given condition.