Separating the vocal and background parts of a piece of music is a very difficult task. In the literature, the process of separating vocal and background parts from musical pieces usually utilizes music repetition feature. In both Repeating Pattern Extraction Technique (REPET) and Robust Principal Component Analysis (RPCA) methods, which are among the leading studies in this field, musical pieces are separated as vocal and background music by using repetition feature of the background music. In this paper, a research study is carried out combining REPET and RPCA algorithms in order to improve the separation performance of the REPET algorithm. In order to compare performances of the proposed method with REPET and RPCA, two different tests have been carried out with selected audio tracks from the MIR-1K dataset. It has been shown by both tests that the performance of the proposed method is much better than other two methods.