The Triangulation Problem for Input-Output Matrices has been intensively studied in order to understand the complex series of interactions among the sectors of an economy. The problem refers to finding a simultaneously permutation of rows and columns of a matrix such as the sum of the entries which are above the main diagonal is maximum. This is a linear ordering problem – a well-known NP-hard combinatorial optimization problem. A new hybrid heuristic based on ant algorithms is proposed to efficiently solve the triangulation problem. Starting from a greedy solution, the proposed model hybridizes the Ant Colony System (ACS) metaheuristic with an Insert-Move (IM) local search mechanism able to refine ant solutions. The proposed ACS-IM algorithm is tested with good results on some real-life economic data sets.