The ferritic matrix in the Fe-22Cr-5Ni-3Mo-0.03C ferritic-austenitic duplex stainless steel can undergo a variety of decomposition processes when aged in the temperature range 550-650degreesC. These processes are the precipitation of the gamma(s) austenitic bi-crystal, the alpha'-BCC ferrite, the tau-phase and the heavily faulted R-phase. The latter is a Frank-Kasper phase, which nucleates on the dislocations in the ferritic delta-matrix and adopts a lenticular shape. This study is basically focused on this intermetallic R-phase. The crystal structure and the chemical composition are respectively studied by electron microdiffraction and energy dispersive X-ray spectroscopy. The R-phase is oriented with respect to the surrounding ferritic matrix by developing a rational orientation relationship such that: (0 0 0 1)(R)//(1 1 1)(delta) with [1 (3) over bar 2](delta)//[2 (1) over bar (1) over bar 0](R). This orientation relationship is here examined in term of lattice matching. Based on this orientation, the morphology and the variant number of this R-phase are understood in terms of the group theory. The defects, present in a large density in the R-phase, are identified as planar faults, which are grouped in two families parallel respectively to {1 3 9}(delta) and {11 13 23}(delta) lattice planes of the ferritic delta-matrix. Based on the obtained results, a structural proximity between the R-phase and a supercell derived from the ferritic matrix has been brought to light. It has been stated that Mo is an efficient R-phase forming element. The results provide valuable insights into the precipitation mechanism associated with the R-phase formation.