The relativistic covariance of the four-vector of the total energy-momentum of a macroscopic body that, in its rest frame, carries general stationary macroscopic charge and current distributions is demonstrated in explicit detail using the balancing of the forces in the body, the existence of hidden mechanical momentum, and the Lorentz-transformation properties of the energy-momentum four-tensors of the "mechanical" and "electromagnetic" parts of the system. (C) 1998 American Association of Physics Teachers.