  We study ballistic transport of spin-polarized electrons through quantum
wires in which the strength of the Rashba spin-orbit interaction (SOI) is
spatially modulated. Subband mixing, due to SOI, between the two lowest
subbands is taken into account. Simplified approximate expressions for the
transmission are obtained for electron energies close to the bottom of the
first subband and near the value for which anticrossing of the two lowest
subbands occurs. In structures with periodically varied SOI strength, {\it
square-wave} modulation on the spin transmission is found when only one subband
is occupied and its possible application to the spin transistor is discussed.
When two subbands are occupied the transmission is strongly affected by the
existence of SOI interfaces as well as by the subband mixing.
