A new blind sequences synchronization method in multiuser multirate CDMA context is proposed in this paper. Instead of the approach based on the Frobenius square norm behaviour (FSNB) previously proposed in [1]-[3], we develop a new blind method based on the maximum eigenvalue behaviour (MEVB) according to analysis window shifts. Theoretical analysis shows that the MEVB-based criterion provides a significant improvement of performances, and proves that it is a powerful tool for blind synchronization. We show that the improvement is mainly due to suppression of synchronisation peaks masking that occurred with the previous method. Simulation results confirm that, performing the synchronization process using this new criterion, allows one to achieve very good performances at the receiver side in term of chip error rate (CER) and bit error rate (BER), even at very low SNRs.