The conserved nine-fold structural symmetry of the centriole is thought to be generated by cooperation between two mechanisms, one dependent on and the other independent of the cartwheel, a sub-centriolar structure consisting of a hub and nine spokes. However, the molecular entity of the cartwheel-independent mechanism has not been elucidated. Here, using Chlamydomonas reinhardtii mutants, we show that Bld10p/Cep135, a conserved centriolar protein that connects cartwheel spokes and triplet microtubules, plays a central role in this mechanism. Using immunoelectron microscopy, we localized hemagglutinin epitopes attached to distinct regions of Bld10p along two lines that connect adjacent triplets. Consistently, conventional and cryo-electron microscopy identified crosslinking structures at the same positions. In centrioles formed in the absence of the cartwheel, truncated Bld10p was found to significantly reduce the inter-triplet distance and frequently form eight-microtubule centrioles. These results suggest that the newly identified crosslinks are comprised of part of Bld10p/Cep135. We propose that Bld10p determines the inter-triplet distance in the centriole and thereby regulates the number of triplets in a cartwheel-independent manner.