The invention relates to an intermediate element for the arrangement of a probe pin with respect to the probe pin carrier of a coordinate measuring machine, having a single-piece base body with a probe pin end and a machine end. It is provided here that the machine end is provided with a coupling element and with a means for ensuring a reproducible rotational alignment, and the probe pin end has a bearing face which is inclined in a fixed manner with respect to the axis of the coupling element, is provided on a general ball segment form which is flattened by the bearing face, and is configured with a positively locking means and/or frictional means for the positively locking and/or frictional engagement with a fastening end of the probe pin in contact with the bearing face.