  We study striped states in the quantum Hall system around half-filled high
Landau levels and obtain the optimal orientation of the striped state in the
presence of an external unidirectional periodic potential. It is shown that the
optimal orientation is orthogonal to the external modulation in the Coulomb
dominant regime (the orthogonal phase) and is parallel in the external
modulation dominant regime (the parallel phase). The phase boundary of these
two phases is determined numerically in the parameter space of the strength and
wave number of the external modulation at the half-filled third Landau level.
