The　chromatically　uniqueness　of　bipartite　graphs　K　(m,　n)　-　A　(　|　A　|　=　2)　was　studied.　With　comparing　the　numbers　of　partitions　into　r　color　classes　of　two　chromatically　equivalent　graphs,　one　general　numerical　condition　guaranteeing　that　K(m,　n)　-　A　(　|　A　|　=　2)　is　chromatically　unique　were　obtained.　This　covers　and　improves　the　former　correlative　results.