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CA (Carrier aggregation) is one of the most important techniques for LTE-Advanced system because of its capability to support wide bandwidth while achieving backward compatibility. In order to improve performance of control information transmission, cross-carrier scheduling is to be supported, i.e. control information on one CC (Component Carrier) can assign radio resource on another CC. Design of search space, in which control information is mapped, for different CCs is one of the most essential issues of cross-carrier scheduling. This paper presents two novel methods of search space design. In the first method, UE (User Equipment)-specific offset is introduced among search spaces of different CCs. Due to the UE-specific offsets, search spaces of different UEs are staggered with each other and probability that search space of one UE is wholly overlapped with that of another UE can be greatly reduced. In the second method, a novel randomization scheme is proposed to generate independent hashing functions for search spaces of different CCs. Because of ideal randomization of the proposed method, search space overlapping of different UEs is reduced. Simulation results show the proposed methods can effectively reduce blocking probability compared with existing methods.