  We investigate the influence of a perpendicular magnetic field on the
spectral and spin properties of a ballistic quasi-one-dimensional electron
system with Rashba effect. The magnetic field strongly alters the spin-orbit
induced modification to the subband structure when the magnetic length becomes
comparable to the lateral confinement. A new subband-dependent energy splitting
at k=0 is found which can be much larger than the Zeeman splitting. This is due
to the breaking of a combined spin orbital-parity symmetry.
