The stepwise height-adjustable mechanism consists of an external box C-section profile (1) in which C-section profile (2) of smaller dimension is slidable. On the inner profile (2) the edges of the gap (6) are provided at chosen distances with circular cutouts (7) working together with a sliding block assembly (3) operated by lever (9). The sliding block element (3) comprises a cylindrical part of a dia. corresponding with the circular cutouts and has two opposite flattenings with a distance equal to the distance between the edges of gap (6). At one position of the lever (9) the flattenings are parallel with the gap allowing it to slide. When the lever is to be turned by 90 deg. this is only possible when one of the cutouts coincides with the sliding block and a flange element at the inner end of the sliding block provides the arresting of the C-section in the selected position.