In this study, they authors introduce a suboptimal training sequence for burst-mode continuous phase modulation. The optimum training sequence has been prove to be optimal for the estimates of carrier frequency offset, carrier phase error and timing error. However, the optimum sequence brings high side-lobe of the log-likelihood function (LLF), that is not benefit for detecting the start of the sequence (SOS). Thus, the suboptimal sequence is designed to improve the SOS performance through decreasing the side-log effect of the LLF. Meanwhile, the proposed sequence can minimise the Cramer-Rao bound for the joint estimation of carrier frequency offset, carrier phase error and symbol timing error. The data-aided maximum likelihood algorithms for timing error and phase error estimation are derived for evaluating the performance of the proposed sequence. The simulation results demonstrate that the new sequence provides better performance on start detection of the sequence than the optimal one. The performance of timing and carrier phase recovery is also close to the ideal synchronisation performance.