  We study topologically stable non-Abelian global vortices in the U(N) linear
sigma model. The profile functions of the solutions are numerically obtained.
We investigate the behaviour of vortices in two limits in which masses of
traceless or trace parts of massive bosons are much larger than the others. In
the limit that the traceless parts are much heavier, we find a somewhat bizarre
vortex solution carrying a non-integer U(1) winding number 1/\sqrt{N} which is
irrational in general.
