Coordinate measuring machines (CMMs) play a leading role in today's industry. As measuring devices, their calibration is an important issue. There are several methods and correspondent artefacts to achieve this goal. However, most methods demand expensive tools and specially skilled operators able to perform complex procedures. So, in order to obtain a reliable calibration method both cheap and easy to implement, we developed a new calibration procedure, grounded on the use of a new artefact, which can be seen as a simplification of the hexapod machine. This is a rigid artefact and the error measurement method is based on the comparison between its measured and real known geometries. The main idea behind this process is to regard the machine errors as hexapod movements. This artefact is the main tool of a new method to obtain the local errors of the CMM. The local calibration permits the determination of the transfer function characterizing the sensor displacement of the CMM. This local calibration consists essentially on the measurement of a rigid artefact having a known geometry, derived from the hexapod geometry, which allows us to determine the errors of displacement of the sensor of the CMM. In this paper, we describe the developed artefact as well as the referring mathematical models, which are obtained from the general equations that model hexapod's behaviour and we state how the error measurement is done. We also present some experimental results, achieved with an uncalibrated built prototype, for the local errors of a CMM Leitz PMM 866, describing in its very course the required procedure. We conclude that the results are compatible with the existing methods and artefacts.