  We study unconstrained control of a two-level quantum system and analyse
critical points of the objective functional which represents quantum average of
system observable at some final time $T$. In Proc. Steklov Inst. Math. 285,
233-240 (2014) it was shown that all maxima and minima of the objective
functional are global if $T\ge \pi$ (in suitable units). In the present work we
show that all maxima and minima are global as soon as $T\ge \pi/2$. Hence we
reduce by the factor of two the minimal time for which traps, i.e., local but
not global maxima or minima of the objective functional, do not exist.
