Let T be a tree and consider the Randić index χ (T)=∑ _ vi-vj (1/δ (v_i) δ (v_j))), where vi–vj runs over all edges of T and δ (vi) denotes the degree of the vertex vi. Using counting arguments we show that the Randić index, is monotone increasing over the well (lexicographic order) ordered sequence of trees with unique branched vertex.