Despite the large improvements in the field of high speed machining, manual polishing operations are still necessary to achieve high quality surfaces named mirror for mould and dies or prosthesis parts. This paper deals with the description of a new polishing method performed on a 5-axis machine. This method is based on the use of an abrasive discs mounted on an flexible rotating tool describing trochoidal trajectories. Firstly, the influence of each polishing parameter on the surface roughness is highlighted on a conventional polishing machine currently used in material sciences. Based on this knowledge, a specific application concerning the polishing of a stainless medical prosthesis is detailed in order to get a mirror surface roughness which Ra is less than to 50 nm.