Carbon nanotubes (CNTs) are one of the strongest known materials. When assembled into fibres, however, their strength becomes impaired by defects, impurities, random orientations and discontinuous lengths. Fabricating CNT fibres with strength reaching that of a single CNT has been an enduring challenge. Here, we demonstrate the fabrication of CNT bundles (CNTBs) that are centimetres long with tensile strength over 80 GPa using ultralong defect-free CNTs. The tensile strength of CNTBs is controlled by the Daniels effect owing to the non-uniformity of the initial strains in the components. We propose a synchronous tightening and relaxing strategy to release these non-uniform initial strains. The fabricated CNTBs, consisting of a large number of components with parallel alignment, defect-free structures, continuous lengths and uniform initial strains, exhibit a tensile strength of 80 GPa (corresponding to an engineering tensile strength of 43 GPa), which is far higher than that of any other strong fibre.