In the blind beamforming technique utilizing self-coherence properties of GPS signals, the covariance matrices estimated from sample data, including the transition between two adjacent bits, suffer from performance degradation. In this letter, we propose the estimation of the covariance matrices using the sample blocks, which are free from the bit transitions under different times of arrival of multiple GPS signals. It combines with the robust cross-SCORE algorithm to suppress the GPS interference. It is shown that an efficient combination of two algorithms is capable of providing high gains to multiple GPS signals simultaneously, while suppressing strong interference.