Reducing the kinematic errors is an important problem in five-axis machining. Errors of this type substantially affect the quality of the five-axis manufacturing. In this paper, we propose and analyse a new numerical algorithm to reduce the kinematic errors of a five-axis tool path using minimisation of the variation of the rotation angles. Our algorithm finds the locations of the cutter contact points (CC points) in the angular space and the orientation/location of the target surface relative to the mounting table that minimise the angle variation. We show through the numerical experiments and cutting simulations that the proposed method is efficient and accurate.