The authors of this paper present an O(nm) approximation algorithm which solves the problem of connecting m signal nets for a set of n terminals laying on the sides of a rectangle such that the total area is minimized. The solution generated by the algorithm has an area ≤.69MC *OPT, where OPT is the area of an optimal solution. Some of the nets are routed by a simple greedy strategy, while the others are handled by several different strategies. In this way, a nonempty set of feasible solutions is produced, from which one with least area is selected. The first steps of the algorithm and the proofs of some lemmata are based on results of [1]; it would be useful to read that paper first.