  It is well known that the topology of Su-Schrieffer-Heeger(SSH) model, which
belongs to AIII symmetry class, is protected by chiral symmetry. In this
article, instead of chiral symmetry, we constrain the bulk Hamiltonian by a
magnetic point group symmetry, which can be generated by a unitary symmetry and
an anti-unitary symmetry. Under these symmetries, a four-band model can be
block diagonalized into two 2-band models and each 2-band model is analogous to
an SSH model. As the two 2-band models are individual, we call the four-band
model double independent SSH (DISSH) model. Interestingly, since the symmetry
requirements of DISSH model can be fulfilled in ferromagnetic systems, the
discovery in this manuscript extends SSH model into ferromagnetic systems.
Furthermore, we presented an example of DISSH model with a set of reasonable
parameters to show that it is possible to manipulate the topological phase of
DISSH model by tuning the magnetic moment in experiment.
