We introduce a variation of \(\sigma\)-labeling to prove that every disconnected unicyclic bipartite graph with eight edges decomposes the complete graph \(K_n\) whenever the necessary conditions are satisfied. We combine this result with known results in the connected case to prove that every unicyclic bipartite graph with eight edges other than \(C_8\) decomposes \(K_n\) if and only if \(n \equiv 0, 1 \pmod{16}\) and \(n > 16\).