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An algorithm for reducing the influence of geometrical, thermal, kinematic and stiffness errors in five-axis machine tool components on the desired tool position and orientation is given. This new algorithm is based on the calculation of the cutting tool error matrix for orthogonal machine tools. In the new model of this matrix, all angular errors of the machine links are considered as infinitesimal rotations. The error matrix is a function of the commanded machine component positions and the errors in these positions. To correct errors in the three translational and two angular tool positions, a matrix of commanded tool position and orientation is multiplied by the inverse error matrix in every period of the tool trajectory interpolation. This corrected matrix of the tool position and orientation provides the inverse kinematics used for calculation of the successive links positions required for achieving the given tool trajectory. The control algorithm for five-axis machine tools with the error compensation is implemented both in the CNC system and in the postprocessor. The proposed algorithm is applied on a vertical five-axis turning centre with two translational and three rotational axes. Twenty-four errors that could cause inaccurate machining are recognised on this machine. The machine links and their coordinate frames are denoted using the Denavit-Hartenberg parameters. © 2013 Taylor & Francis.