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The cyclostationary feature detector is a viable candidate for a primary user (PU) detection method of the cognitive radio (CR) system. However, it requires very long detection time, which leads to inefficient spectrum utilization. To reduce the detection time, we propose to apply the sequential detection framework to the cyclostationary feature detector. Unfortunately, a straightforward application cannot achieve a sufficient gain, which is expected with the sequential detection. To solve this problem, we design a novel detector, taking account of the cyclic phase of the cyclostationary signal. The simulation results show that the proposed detector reduces the average detection time almost in half. The proposed detector can well be applied to the CR systems that operate in the frequency bands, where the PUs have long interarrival and sojourn time. For example, the CR systems equipped with the proposed detector can efficiently exploit the white space in the VHF/UHF TV bands.