  To a phenomenological core described by the Generalized Coherent State Model
a set of interacting particles are coupled. Among the particle-core states one
identifies a finite set which have the property that the angular momenta
carried by the proton and neutron quadrupole bosons and the particles
respectively, are mutually orthogonal. The magnetic properties of such states
are studied. All terms of the model Hamiltonian satisfy the chiral symmetry
except for the spin-spin interaction. There are four bands of two
quasiparticle-core dipole states type, which exhibit properties which are
specific for magnetic twin bands. Application is made for the isotopes $^{188,
190}$Os.
