  We investigated the relativistic dynamics of oppositely charged two fermions
interacting with an external uniform magnetic field. We chose the interaction
of each fermion with the external magnetic field in the symmetric gauge, and
obtained a precise solution of the corresponding fully-covariant two-body Dirac
equation that derived from Quantum Electrodynamics via Action principle. The
dynamic symmetry of the system we deal with allowed us to determine the
relativistic Landau levels of such a spinless composite system, without using
any group theoretical method. As a result, we determined the eigenfunctions and
eigenvalues of the corresponding two-body Dirac Hamiltonian
