Summary: By using the method of semi-tensor product of matrices, the controllability and observability of \(k\)-valued control networks are investigated. A controllability matrix is constructed by eigenfunctions and a novel necessary and sufficient condition for controllability is given. The new condition simplifies computational complexity of original conditions, and the highest power of matrix is reduced from \(k^{n+m}\) to \(k^n\). Also, a sufficient condition for observability is obtained, which can be computed easily.