In the last mitotic division of the epidermal lineage in the ascidian embryo, the cells divide stereotypically along the anterior-posterior axis. During interphase, we found that a unique membrane structure invaginates from the posterior to the centre of the cell, in a microtubule-dependent manner. The invagination projects toward centrioles on the apical side of the nucleus and associates with one of them. Further, a cilium forms on the posterior side of the cell and its basal body remains associated with the invagination. A laser ablation experiment suggests that the invagination is under tensile force and promotes the posterior positioning of the centrosome. Finally, we showed that the orientation of the invaginations is coupled with the polarized dynamics of centrosome movements and the orientation of cell division. Based on these findings, we propose a model whereby this novel membrane structure orchestrates centrosome positioning and thus the orientation of cell division axis.