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This paper discusses the overall positioning accuracy of a neurosurgical robot system. First, the overall positioning accuracy of the robot system is analyzed and formulated. Then, the efforts are focused on improving the positioning accuracy of the robot arm. A revised Denavit--Hartenberg (D-K) kinematic model is addressed to describe two nearly parallel joint axes for the calibration of the robot. The joint transmitting error of the robot is compensated by using a backpropagation (BP) neural network. Finally, the absolute positioning accuracy of the robot arm is measured. A phantom is designed to simulate the clinical workflow of the robot-assisted neurosurgery for measuring the overall positioning accuracy of the robot system. The results show that the positioning error of the robot arm is less than 1 mm, which is comparable to that of stereotactic frames; and that the overall positioning error of the robot system is caused mainly by target registration error, which proves the effectiveness of our efforts.