New ways to increase the performance of metal cutting are constantly being sought. Although diverse and increasingly performing tools are designed and used, especially those with inserts, rarely new processing schema are identified in order to ensure favourable conditions to obtain a higher quality for generated surfaces. The paper presents a particular and innovative processing schema, as well as a specific tool for machining cylindrical surfaces by turning with a tangential cutting line. The active part of the latter is an insert whose cutting line is placed frontally in a vertical plane and considerably inclined in relation to the horizontal plane. In order to validate the concept, a variation of the tool has been developed and tested, one that doesn’t present the option of adjusting the angle of the cutting line. The success thus achieved prompted the design of a tool that allows the cutting line to be tilted at any angle in relation to the horizontal plane. A patent application has been filed in this regard.