  We study a new class of N=1 supersymmetric orientifolds in six space-time
dimensions. The world-sheet parity transformation is combined with a
permutation of the internal complex coordinates. In contrast to ordinary
orientifolds the twisted sectors contribute to the Klein bottle amplitude
leading to new tadpoles to be cancelled by twisted open string sectors. They
arise from open strings stretched between D7-branes intersecting at non-trivial
angles. We study in detail the Z_3, Z_4 and Z_6 permutational orientifolds
obtaining in all cases anomaly free massless spectra.
