A position of a turntable axis is repeatedly determined in the device coordinate system of a coordinate measuring device. A test body on the turntable is probed in a plurality of turntable positions in order to determine the X and Y coordinates of the turntable axis in the device coordinate system from the contact points. In addition, a first contact body reference point that is stationary relative to the X-axis and disposed next to the turntable is probed to determine its X coordinate. Similarly, a second contact body reference point that is stationary relative to the Y-axis is probed to determine its Y coordinate. These steps are repeated at one or more later points in time to repeatedly determine the X coordinate and the Y coordinate of the turntable axis from the X coordinate of the first contact-body reference point and the Y coordinate of the second contact-body reference point.