Unlike the traditional Hermitian system, a non-Hermitian system has exceptional points. When one parameter evolves to an exceptional point, a phase transition occurs in the non-Hermitian system, i.e., two eigenstates collapse and their corresponding eigenvalues merge into one. The two-state and four-state non-Hermitian systems are studied by using the coupled metamaterial artificial atoms. Various evolution traces of the eigenvalues of non-Hermitian systems are studied by recording the variation of peak frequency of coherent absorption with the loss parameter in an open system for electromagnetic waves. Theoretical and electromagnetic-field simulated results show that, five kinds of exceptional points can form by different combination ways of eigenstates in the four-state non-Hermitian system. Among them, the exceptional points at which more than two eigenstates merge is called as high-order exceptional points.