  We investigate the direct contribution of the magnetic field to the
gravitational wave generation. To do so, we study the post-Newtonian
energy-momentum tensor of the magnetized fluid and the post-Newtonian expansion
of the gravitational potential in the wave zone. We show that the magnetic
field appears even in the first post-Newtonian order of the multipole moment
tensor. Then, we find an explicit relativistic correction containing the
magnetic field contribution to the well-known quadrupole formula. As an
application of this derivation, we find that the B-field part of the
gravitational waves released in the early stages of a millisecond magnetar's
life can be as much as one-hundredth of the signals due to the deformed
rotating neutron stars. We show that although the event rate of this system is
small, the signal would lie in the sensitivity range of the next generation of
detectors.
