A device for coupling two shafts by a gear mechanism includes a coupling part ending one of the two shafts. The coupling part is fitted concentrically into a complementary coupling part ending the other shaft. Splines of the coupling part have a constant profile along a median zone of the coupling part and which, in a first zone in continuation of the median zone, has a smaller thickness, between flanks of a spline, than a maximum thickness of the same spline in the median zone. Splines of the coupling part continue, beyond the first zone, as far as a centering zone on the same side as the first zone. The splines and the spline bottoms have, in the coupling zone between the centering zone and the first zone, a profile that continuously couples the splines and the spline bottoms to the surface of the centering zone.