This paper describes a new calibration method for robots. Based on the fact that most industrial robots have very good repeatability, and hence their positioning errors have corresponding repeatability, the method focuses on finding continuous functions of robot joint variables to describe robot positioning errors. These functions are then used for position compensation. Therefore, the method is different from the conventional calibration methods which emphasize robot geometry parameter errors. Since the number of unknowns in the new calibration method is less than that in conventional approaches, the new method shows the advantage of simplicity as well as accuracy. In this research, both computer simulations and experiments involving SCARA robots have been conducted. The experimental results clearly verify the effectiveness of the method. Robot accuracy can be improved to less than 0.3 mm Cartesian space error from relatively large initial errors. Because robot end effector position errors can be measured in a user defined frame, the measurement equipment is readily available and measurements can be automatically conducted with a developed robot program, this method is very practical, economical and efficient.