Abstract. The Randic index is defined as the sum of 1/(deg_G(u)deg_G(v))^1/2, taken through all the edges of G. Recently, some problems for Randic index were successfully attacked using another parameter, namely the sum of 1/(max(deg_G(u),deg_G(v))). In this paper we study this new parameter. Among others, we determine the graphs with minimal and maximal values of this parameter among unicyclic graphs and trees.