Summary: ``The Hamiltonian properties of the second-order circuit graphs of general connected matroids are studied in the paper. The complete bipartite graphs $K_{2, n}$ and $K_{3, n}$ are selected for discussion to prove the Hamiltonian property of the second-order circuit graphs of the two kinds of circuit matroids and the connectivity and pancyclic property of the second-order circuit graphs of the two kinds of circuit matroids and the connectivity and pancyclic property of the second-order circuit graphs of the circuit matroids of $K_{2,n}$. Also, a conjecture on the consistent Hamiltonian property of the second-order circuit graphs of the circuit matroids of $K_{2,n}$ and $K_{3,n}$, is proposed in the paper.''