A stylet unit has a flexible tubular stylet sleeve, a flexible inner stylet wire inserted into a channel of the stylet sleeve with at a least a portion of the stylet wire and at least a portion of the channel each having a non-circular cross section for preventing rotation of the wire inside the sleeve. The stylet unit has a handle with which the sleeve and the stylet wire are movable relative to each other in a longitudinal direction. The sleeve and the wire are connected at one end thereof to the handle, with the sleeve being rotationally arranged within the handle.