A lot of works are dedicated to studying different mathematical models of competition with goal of determining conditions under which two or more species can coexist when in conflict with one another. Some of these works are [1-5]. Usually results are represented in form of bifurcation diagrams and basins of attraction. We suggest to use for bifurcation analysis of the discrete models the method of complete bifurcation groups (MCBG) [6-9]. The method originally was worked out for systems described by ODE, but it is based on replacement of continuous phase trajectories with a discrete set of points of stroboscopic map. So, this means we can apply the method to discrete systems [9]. Method of complete bifurcation groups consist in direct numerical simulation of original nonlinear model, that is, without its simplification. Under the method of complete bifurcation groups we understand complex of approaches to analysis of dynamic systems, which involves the following procedures: at fixed system parameters – constructing of periodic skeleton, i.e. search of all periodic stable and unstable regimes and bifurcation subgroups with unstable periodic infinitiums (UPI) on plane of states, and constructing of regimes' basins of attraction on plane of states; at varying system parameters – constructing of one and two parameters bifurcation diagrams. The main feature of the MCBG is nT-solution branches continuation without their break in bifurcation points. New bifurcation sub-groups, obtained by the MCBG, such as complex protuberances and unstable periodic infinitiums (UPI) allow predicting and finding new (unknown) regular and chaotic attractors in the models [6-9]. Continuation on unstable branches of the periodic regimes allows also finding new so-called rare attractors (RA), which don't succeed to find systemically by other methods. Rare attractors are stable periodic regimes, which exist only in the relatively narrow intervals of the change of variable parameter. Rare attractors may be periodic, quasi-periodic or chaotic. They may belong to five different types such as tip, island, dumb-bell, hysteresis and protuberance. So, unstable periodic solutions and their continuation on parameter have corner-stone meaning in the MCBG. This paper is devoted to implementation of the method of complete bifurcation group to numerical bifurcation analysis of discrete two-species competition model. There were found rare periodic and chaotic attractors and parameter range with coexisting rare and chaotic attractors.