We propose a new algorithm to extract the fetal electrocardiogram (FECG) from a multi-channel electrocardiogram (ECG) recorded at the chest and abdomen of a pregnant woman. To extract the FECG from the composite abdominal ECG, the classical time-domain method based on singular value decomposition (SVD) has been generally used. However, this method has some disadvantages, such as its high degree of computational complexity and the necessary assumption that vectors between the FECG and the maternal electrocardiogram (MECG) should be orthogonal. The proposed algorithm, which uses SVD in a discrete cosine transform (DCT) domain, compensates for these disadvantages. To perform SVD with lower computational complexity, DCT coefficients corresponding to high-frequency components were eliminated on the basis of the properties of the DCT coefficients and the frequency characteristics of the FECG. Moreover, to extract the pure FECG with little influence of the direction of the vectors between the FECG and MECG, three new channels were made out of the MECG suppressed in the composite abdominal ECG, and the new channels were appended to the original multi-channel ECG. The performance of the proposed algorithm and the classical time-domain method based on SVD were compared using simulated and real data. It was experimentally verified that the proposed algorithm can extract the pure FECG with reduced computational complexity.