The Randić index R(G) of a graph G is the sum of the weights (dudv)− 1 2 of all edges uv in G, where du denotes the degree of vertex u. Du and Zhou [On Randić indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 2760–2770] determined the n-vertex trees with the third for n ≥ 7, the fourth for n ≥ 10, the fifth and the sixth for n ≥ 11 maximum Randić indices. Recently, Li et al. [The Randić indices of trees, unicyclic graphs and bicyclic graphs, Ars Comb. 127 (2016), 409–419] obtained the n-vertex trees with the seventh, the eighth, the ninth and the tenth for n ≥ 11 maximum Randić indices. In this paper, we correct the ordering for the Randić indices of trees obtained by Li et al., and characterize the trees with from the seventh to the sixteenth maximum Randić indices. The obtained extremal trees are molecular and thereby the obtained ordering also holds for molecular trees