5-axis high speed machine tools are widely used in industry. The axis movements are generated by the Computer Numerical Controller (CNC) which has to transform the part program into a sequence of axis setpoints. Most of the time, the tool path is described with linear segments (G1) which lead to tangency discontinuities between blocks. With acceleration and jerk limitations, these discontinuities will induce a zero feedrate and thus surface marks and an increase in machining time. The aim of this paper is to study a 5-axis corner smoothing method required to obtain a C2 continuous tool path geometry. Several methods have been developed in 3-axis but the 5-axis corner smoothing is still a challenge. To smooth the tool tip position and the tool orientation, the 5-axis tool path is represented by two B-Spline curves. The proposed corner smoothing model allows to control the contour and orientation tolerances in the workpiece coordinate system. The main difficulty is to obtain a C2 continuous connection between the initial tool path and the newly inserted smoothing portion. This connection is linked to the parametrization of the bottom and top B-Splines. This algorithm can be integrated to a feedrate interpolator to control a 5-axis milling machine equipped with an Open CNC.