This paper considers the 2-maxian location problem on a cactus graph G=(V,E) in which the aim is to find two points on G for establishing obnoxious facilities such that the sum of weighted distances from all vertices (existing clients) to the farthest facility is maximized. We develop a modified algorithm for obtaining an optimal solution of the problem under investigation. The proposed algorithm is based on the generic solution idea by Kang et al., while it is straightforward and takes lower computational operations.