Abstract: In physics, due to the symmetry between electricity and magnetism, physicists believe that magnetic charge exist in nature, similar to electric charges. Although experimental evidence for the existence of magnetic charges has not been found, discussion and exploration of this concept have never ceased. The initial focus of this article is to study the covariant form of the Maxwell's equations in the presence of magnetic charges. To do this, we classify the magnetic field into two types, i.e., Bh generated by magnetic charges and Bt produced by changing electric fields and conduction currents. Then we find that by introducing certain constraints for Bh, we can decompose the Maxwell's equations into the Maxwell's equations without magnetic charges and three additional constraint equations satisfied by Bh. The Maxwell's equations without magnetic charges naturally satisfy the principle of covariance in specail relativity theory, and we will not talk about this. We will study the properties of magnetic charges and their magnetic fields as a new form of matter by the three equations concerning Bh.

Key words:  magnetic charge, Maxwell equations, covariance