Several factors determine the effectiveness of an early-stage artifact removal algorithm for the detection of breast cancer using confocal microwave imaging. These factors include the ability to select the correct time window containing the artifact, the ability to remove the artifact while being robust to normal variances, and ability to effectively preserve the tumor response in the resultant signal. Very few (if any) of the existing artifact removal algorithms incorporate all of these qualities. In this letter, a novel hybrid artifact removal algorithm for microwave breast imaging applications is presented, which combines the best attributes of two existing algorithms to effectively remove the early-stage artifact while preserving the tumor response. This algorithm is compared to existing algorithms using a range of appropriate performance metrics.