In digital modulation for mobile radio telephone services frequency modulation with continuous phase with small modulation indices (MSK/GMSK) is sometimes used. Extension of the synchronization subsystems' pulling band in a coherent receiver and reducing synchronization delay is important for the mobile communication. At this moment there are only two possible synchronization schemes for the coherent MSK/GMSK receiver: Costas and de Buda's. This paper presents a new method (a possible alternative to both of them) where the frequency discriminator with decoupled carrier and bit synchronizing subsystem are combined to handle the task. For comparison, this paper also describes performances of the Costas carrier recovery scheme, which is widely employed for MSK/GMSK coherent demodulation. Discrimination and fluctuation characteristics for frequency, phase, and symbol delay synchronization subsystems are shown and the BER degradation from the conventional Costas scheme is calculated. This paper demonstrates with simulation results that the proposed scheme improves RF carrier acquisition performances, and at the same time, for large signal-to-noise ratios (SNR's) provides similar or better tracking performances than the Costas one. While limited to higher SNR ratios, the proposed synchronization scheme is suitable for many applications and can be implemented with simpler circuitry, well suited to integrated circuit implementation.