Recently, the use of portable electroencephalogram (EEG) devices to record brain signals in both health care monitoring and in other applications, such as fatigue detection in drivers, has been increased due to its low cost and ease of use. However, the measured EEG signals always mix with the electrooculogram (EOG), which are results due to eyelid blinking or eye movements. The eye-blinking/movement is an uncontrollable activity that results in a high-amplitude slow-time varying component that is mixed in the measured EEG signal. The presence of these artifacts misled our understanding of the underlying brain state. As the portable EEG devices comprise few EEG channels or sometimes a single EEG channel, classical artifact removal techniques such as blind source separation methods cannot be used to remove these artifacts from a single-channel EEG signal. Hence, there is a demand for the development of new single-channel-based artifact removal techniques. Singular spectrum analysis (SSA) has been widely used as a single-channel-based eye-blink artifact removal technique. However, while removing the artifact, the low-frequency components from the non-artifact region of the EEG signal are also removed by SSA. To preserve these low-frequency components, in this paper, we have proposed a new methodology by integrating the SSA with continuous wavelet transform (CWT) and the k-means clustering algorithm that removes the eye-blink artifact from the single-channel EEG signals without altering the low frequencies of the EEG signal. The proposed method is evaluated on both synthetic and real EEG signals. The results also show the superiority of the proposed method over the existing methods.