  The two-fermion bound system is an attractive subject of atomic and
sub-atomic physics. Despite these systems are rather simple the study of
two-particle bound states is challenging and still remains a source of progress
in quantum theory. Here we present a new method of solving the Bethe Salpeter
equations for the bound states of spinor particles by using the expansion of
the vertex functions over the complete set of four-dimensional hyperspherical
harmonics. Within this method the BS equation is treated in a ladder
approximation for the cases of scalar, pseudoscalar and vector meson exchanges
with corresponding form factors. This method is shown to be effective and
stable.
