A coordinate measuring machine has a measurement head having a point measurement device which measures first coordinates of only a single point on the surface of a workpiece at a given time. An area measurement device records images of a reference surface. A displacement device displaces the measurement head and/or the workpiece such that they assume different relative positions with respect to one another. An evaluation device calculates a shift between images that the area measurement device has recorded of the reference surface at different times at different relative positions, with a stitching algorithm. Based on this, second coordinates of the measurement head, which are defined relative to the reference surface, are determined. By linking the first coordinates with the second coordinates, third coordinates are determined, which define the points on the surface of the workpiece measured by the point measurement device relative to the reference surface.