A number of techniques have been proposed for the design of tree-structured filter banks matched to the statistics of the input signal. Amongst all of the porposed techniques, a top-down design approach has been rcognized as a computationally efficient method for the design of tree-structured filter banks. However, the conventional top-down technique is sub-optimal. In this paper, we modify the existing top-down design approach to deal with its suboptimal nature. Under certain assumtions, analytical expressions are derived for filter banks of unconstrained lengths that maximize the overall coding gain of the tree-structured filter bank.