  Unlike the Schwarzschild black string in the Randall-Sundrum scenario which
is known to have the geodesics reaching the AdS-horizon terminating there, the
D=7 extremal BPS selfdual string of N=2 gauged supergravity potentially differs
from this result. I give a complete proof that timelike radial trajectories of
the selfdual string solution that escapes to r=\infty do not see a curvature
singularity on the horizon at z=\infty.
