The appearance of the non-homogeneous structures of the indirect exciton density distribution in the region of the quantum well (in the region of the inner ring) is explained. The structure (the fragmentation) occurs due to the exciton condensed phase formation because of interaction between excitons. The formation of the structure is related with the non-equalibrity of the system, which is caused by the exciton finite lifetime and the presence of the pumpimg. The structure emerges in the shape of a set of islands or circles of the condensed phase. The structure type depends on the pumping intensity, the size of the laser spot and disappears with increasing the temperature. The merging of two structures, created by different laser spots, is investigated at decreasing the distance between the centers of the spots.