During cell division microtubules capture chromosomes by binding to the kinetochore assembled in the centromeric region of chromosomes. In mitosis sister chromatids are captured by microtubules emanating from both spindle poles, a process called bipolar attachment, whereas in meiosis I sisters are attached to microtubules originating from one spindle pole, called monopolar attachment. For determining chromosome orientation, kinetochore geometry or structure might be an important target of regulation. However, the molecular basis of this regulation has remained elusive. Here we show the link between kinetochore orientation and cohesion within the centromere in fission yeast Schizosaccharomyces pombe by strategies developed to visualize the concealed cohesion within the centromere, and to introduce artificial tethers that can influence kinetochore geometry. Our data imply that cohesion at the core centromere induces the mono-orientation of kinetochores whereas cohesion at the peri-centromeric region promotes bi-orientation. Our study may reveal a general mechanism for the geometric regulation of kinetochores, which collaborates with previously defined tension-dependent reorientation machinery.