In order to solve the problem of ambiguous acquisition of BOC signals caused by its property of multiple peaks, an unambiguous acquisition algorithm named reconstruction of sub cross-correlation cancellation technique (RSCCT) for BOC(kn, n) signals is proposed. In this paper, the principle of signal decomposition is combined with the traditional acquisition algorithm structure, and then based on the method of reconstructing the correlation function. The method firstly gets the sub-pseudorandom noise (PRN) code by decomposing the local PRN code, then uses BOC(kn, n) and the sub-PRN code cross-correlation to get the sub cross-correlation function. Finally, the correlation peak with a single peak is obtained by reconstructing the sub cross-correlation function so that the ambiguities of BOC acquisition are removed. The simulation shows that RSCCT can completely eliminate the side peaks of BOC (kn, n) group signals while maintaining the narrow correlation of BOC, and its computational complexity is equivalent to sub carrier phase cancellation (SCPC) and autocorrelation side-peak cancellation technique (ASPeCT), and it reduces the computational complexity relative to BPSK-like. For BOC(n, n), the acquisition sensitivity of RSCCT is 3.25 dB, 0.81 dB and 0.25 dB higher than binary phase shift keying (BPSK)-like, SCPC and ASPeCT at the acquisition probability of 90%, respectively. The peak to average power ratio is 1.91, 3.0 and 3.7 times higher than ASPeCT, SCPC and BPSK-like at SNR = – 20 dB, respectively. For BOC(2n, n), the acquisition sensitivity of RSCCT is 5.5 dB, 1.25 dB and 2.69 dB higher than BPSK-like, SCPC and ASPeCT at the acquisition probability of 90%, respectively. The peak to average power ratio is 1.02, 1.68 and 2.12 times higher than ASPeCT, SCPC and BPSK-like at SNR = – 20 dB, respectively.