The problem of optimal design of a pressure relief header network is addressed using an alternative set of decision variables represented by the lengths of pipe segments having different standard diameters. Although these variables have been;largely employed for water distribution network design, until the present moment, they have not been applied to the design of pressure relief networks. The proposed formulation results in a linear programming problem easily solved by standard procedures. This optimization scheme is applied to the design of a network example from the literature. The solution found has a lower cost when compared to previous results.