In this research the behavior of regional GDP per capita is analyzed in order to determine the differences in economic growth through the identification process of economic convergence. This work, based the economic measurement instrumentation from the theory developed by Barro Sala I Martin. In this research, the process of convergence that have presented local authorities,from1970 to 2012 Among the most important results the evidence of convergence between departments has been, the results confirm the existence of absolute convergence for two sub-periods 1976-1982 and 1982-1988.