the outer shroud 4 meet as follows the aerodynamic profile 200 is extended radially beyond the outer shroud in order to account for combined assembly clearances the aerodynamic profile 200 is truncated along a surface 201 parallel to the internal face 5 of the outer shroud 4 the surface 201 and the internal face 5 being separated by a distance j equal to the size of the combined assembly clearances once the aerodynamic profile 200 has been truncated the cutting surface 202 thus obtained is projected radially to obtain a cylinder 203 extending slightly above the outer shroud 4 thus the end of the vane situated between the cutting surface 202 and the internal face 5 of the outer shroud 4 is a cylinder the generatrices of which are parallel to the stacking axis e of the vane this type of connection facilitates the drilling of holes in the outer shroud in which holes the vanes will be positioned fig4 shows a stator section viewed in cross section on a plane containing the axis x of rotation of the turbomachine according to the invention the vane 2 of total height h is made up of a radially external part 10 of height h 1 and of a radially internal part 2 a of height h 4 the radially external part 10 also known as the vane tip is made up of a connecting part 2 b of height h 2 and an intermediate part 2 c of height h 3 with h 1 h 2 h 3 the vane 2 is set radially in the outer shroud 4 by means of its radially external part 10 and more specifically by virtue.