Recently, Wang, Huang, Liu, and Zhang reported experimental and theoretical studies on CnB- (n = 1-13) as well as the CnN- clusters (n = 1-13). They claimed that both clusters (n = 1-13) should be linear chains based on ab initio HF/3-21G geometry optimizations. In the present paper, we report the new results obtained from ab initio calculations at higher levels on the ground states of the CnB- cluster anions. It can be concluded from our calculated results that for the ground states, the linear structures of CnB- up to n = 4 are stable and that those of other CnB- clusters (n = 5-7) are not linear and are very floppy. The vertical electron detachment and fragmentation energies of CnB- (n = 1-7) in their ground states are evaluated with the MP4SDTQ method at the MP2 geometry using 6-31G(d) augmented with a set of diffuse sp functions. The fragmentation energies are also evaluated with the QCISD(T) method using the same basis to verify the convergence of the perturbational results. The calculated fragmentation energies show that the CnB- clusters with even n’s are more stable than those with odd n’s, which is consistent with the observed odd-even alternation of the TOF signal intensities.