GIS- and LTL- (the three capital characters indicate the framework type-code) type zeolites were obtained by organic structure-directing agent free hydrothermal conversion of FAU-type zeolite at 125 degrees C in the presence of NaOH and KOH, respectively. MOR-type zeolite was found coexisting with GIS-type when the hydrothermal conversion with NaOH was carried out at 140 degrees C. There was a common building unit consisting of four-membered ring chain such as d6r, dsc, and dcc (the three characters indicate the composite building unit-code) units present in both the starting zeolite (FAU-type zeolite) and the product zeolites (GIS- and LTL-type zeolites), which was the crucial factor for crystal growth through interzeolite conversion. In the case of severe hydrothermal synthesis conditions such as high temperature, however, the crystallization behavior was similar to that observed in conventional hydrothermal synthesis using amorphous materials because the starting zeolite was excessively decomposed. The hypothesis was confirmed by successful interzeolite conversion of *BEA- to MFI-type zeolite which shared the common composite building unit mor.