The　Correlation　Clustering　Problem　(CorCP)　is　a　significant　clustering　problem　based　on　the　similarity　of　data.　It　has　significant　applications　in　different　fields,　such　as　machine　learning,　biology,　and　data　mining,　and　many　different　problems　in　other　areas.　In　this　paper,　the　Balanced　2-CorCP　(B2-CorCP)　is　introduced　and　examined,　and　a　new　interesting　variant　of　the　CorCP　is　described.　The　goal　of　this　clustering　problem　is　to　partition　the　vertex　set　into　two　clusters　with　equal　size,　such　that　the　number　of　disagreements　is　minimized.　We　first　present　a　polynomial　time　algorithm　for　the　B2-CorCP　on　$M$-positive　edge　dominant　graphs　($M\geqslant　3$).　Then,　we　provide　a　series　of　numerical　experiments,　and　the　results　show　the　effectiveness　of　our　algorithm.