The present work shows the applying of successive H indices in the evaluation of a scientific institution, using the researcher-department-institution hierarchy as level of aggregation. The scientific production covered by the Web of Science of the researcher's staff from the Cuban National Scientific Research Center, during the period 2001-2005, was studied. The Hirsch index (h-index; J.E. Hirsch, 2005) was employed to calculate the individual performance of the staff, using the g-index created by Leo Egghe (2006) and the A-index developed by Jin Bi-Hui (2006) as complementary indicators. The successive H indices proposed by András Schubert (2007) were used to determine the scientific performance of each department as well as the general performance of the institution. The possible advantages of the method for the institutional evaluation processes were exposed.