  We study quantum brachistochrone problem for the spin-1 system in a magnetic
field of a constant absolute value. Such system gives us a possibility to
examine in detail the statement of papers [A. Carlini {\it et al.}, Phys. Rev.
Lett. {\bf 96}, 060503 (2006), D. C. Brody, D. W. Hook, J. Phys. A {\bf 39},
L167, (2006)] that {\it the state vectors realizing the evolution with the
minimal time of passage evolve along the subspace spanned by the initial and
final state vectors.} Using explicit example we show the existence of quantum
brachistochrone with minimal possible time, but the state vector of which,
during the evolution {\em leaves} the subspace spanned by the initial and final
state vectors. This is the result of the choice of more constrained Hamiltonian
then assumed in the general quantum brachistochrone problem, but what is worth
noting, despite that such evolution is more complicated it is still time
optimal. This might be important for experiment, where general Hamiltonian with
the all allowed parameters is difficult to implement, but constrained one
depending on magnetic field can be realized. However for pre-constrained
Hamiltonian not all final states are accessible. Present result does not
contradict general statement of the quantum brachistochrone problem, but gives
new insight how time optimal passage can be realized.
