In this paper, we propose a spectrum splitting-based cognitive interference management method for LTE downlink two-tier networks (that provide closed-access mode). In the proposed method, the resource-blocks in the macrocell (in frequency and time domain) are allocated to the users with the received signal-to-interference-plus-noise-ratio greater than a threshold. The rest of resource-blocks are then allocated to the femtocells. To evaluate the effectiveness of this method, we develop a system level simulation and compare the proposed method with no interference management and also interfering resource blocking-based cognitive interference management method (IRB-CIM). It is shown that the proposed method significantly increases average throughput of femtocells' cell-edges. Furthermore, the simulation results indicate that by adjusting parameters, the proposed method results in higher average throughput for femtocells and for overall system compared to other methods. The proposed method senses control-channel of the macrocell to detect spectrum availability which is simpler and faster than IRB-CIM.