  We study a modification of the fractional analogue of the Brownian meander,
which is Brownian motion conditioned to be positive on the time interval
${[0,1]}$. More precisely, we determine the weak limit of a fractional Brownian
motion which is penalized -- instead of being killed -- when leaving the
positive half-axis. In the Brownian case, we give a representation of the
limiting process in terms of an explicit SDE and compare it to the SDE
fulfilled by the Brownian meander.
