  An axial next-nearest-neighbor Ising (ANNNI) model is studied by using the
non-equilibrium relaxation method. We find that the incommensurate stripe phase
between the ordered phase and the paramagnetic phase is negligibly narrow or
may vanish in the thermodynamic limit. The phase transition is the second-order
transition if approached from the ordered phase, and it is of the
Kosterlitz-Thouless type if approached from the paramagnetic phase. Both
transition temperatures coincide with each other within the numerical errors.
The incommensurate phase which has been observed previously is a paramagnetic
phase with a very long correlation length (typically $\xi\ge 500$). We could
resolve this phase by treating very large systems ($\sim 6400\times 6400$),
which is first made possible by employing the present method.
