New electromagnetic conservation laws

The Chevreton superenergy tensor was introduced in 1964 as a counterpart, for electromagnetic fields, of the well-known Bel-Robinson tensor of the gravitational field. We here prove the unnoticed facts that, in the absence of electromagnetic currents, Chevreton's tensor (i) is completely symmetric, and (ii) has a trace-free divergence if Einstein-Maxwell equations hold. It follows that the trace of the Chevreton tensor is a rank-2, symmetric, trace-free, {\em conserved} tensor, which is different from the energy-momentum tensor, and nonetheless can be constructed for any test Maxwell field, or any Einstein-Maxwell spacetime.