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A novel, fully automated high-stability, high-eigenfrequency scanning tunnelling microscope (STM) has been developed. Its key design feature is the application of two piezoelectric ceramic tubes, one for the x-y-z motion of the tip and one for a linear motor ('nano-worm') used for the coarse positioning of the tip relative to the specimen. By means of the nano-worm, the tip can be advanced in steps between 16 and 0.2 nm. The walking distance is greater than 2 mm, with a maximum speed of 2000 steps/s. The nano-worm positioning implies that this STM is fully controlled by electronic means, and that no mechanical coupling is needed, which makes operation of the STM extremely convenient. The axial-symmetry construction is rigid, small and temperature-compensated, yielding reduced sensitivity to mechanical and acoustic vibrations and temperature variations. The sample is simply placed on a piece of invar which surrounds the scanner tube and the nano-worm and is held by gravity alone. This allows for easy sample mounting. The performance of the microscope has been tested in air by imaging a variety of surfaces, including graphite and biological samples.