Spectrum sensing is of paramount importance in the Cognitive Radio Network (CRN) due to massive spread of wireless services. However, spectrum sensing in CRN is affected by multipath effects that make detection difficult. Square- Law Combining (SLC) technique, which is one of the methods previously used to address this problem, is associated with hardware complexity that results in long processing time. Hence, this paper aim to modify SLC technique for primary user detection in the CRN. The modified model consists of three Secondary User (SU) antennas which receive the faded signals through the Rayleigh fading channel. The received signals are combined using Switch Combiner (SC) at Radio Frequency (RF) stage. The selected signal passes through only one Energy Detector (ED) before making decision. The modified model is incorporated into simulation model which consists of Primary User (PU) transmitter that processes the randomly generated data through some signal processing techniques for transmission to the SU receiver. Probability of False Alarm (PFA) expression is derived for the modified Square-Law Combiner (mSLC) to set the thresholds at 6.64 and 9.14 for PFA of 0.01 and 0.02, respectively. The modified model is evaluated using Probability of Missing (PM), Probability of Detection (PD) and Processing Time (PT) to determine the performance. The results of the mSLC show that at SNR of 4 dB and PFA of 0.01, the values obtained for PD, PM, PT are 0.6575, 0.3530, 5.5540 s, respectively, as against the conventional SLC of 0.4000, 0.600, 6.2055 s, respectively. At SNR of 4 dB and PFA of 0.02, the values obtained for the mSLC are 0.7600, 0.3457, 6.1945 s for PD, PM and PT, respectively, as against 0.4000, 0.6000, 7.2197 s for conventional SLC. The results show that mSLC gives lower PM, higher PD and lower PT values when compared with conventional SLC.