Exchange bias results are reported on Co/CoO nanotriangles prepared by depositing ultra-thin (10nm) ferromagnetic Co film using molecular beam epitaxy on polystyrene nanospheres (530nm). Then the surface was exposed to oxygen under high vacuum conditions to form antiferromagnetic CoO layer on top. After liftoff of these nanospheres, well defined triangles array was seen. For comparison, a similar film was simultaneously deposited on plane Si (100) substrate. Magnetization measurements carried out at room temperature with different orientations of magnetic field show that the nanotriangles exhibit higher coercivity as compared to that of the film deposited on plane substrate (in parallel direction). However, in perpendicular direction, lesser coercivity is observed in triangular film. In this case, the exchange bias measurements carried out after field cooling reveal a lesser exchange bias field for Co/CoO triangles as compared to that of continuous film. These observations are attributed to the thermally unstable nature of triangles where thermal fluctuation flips the AFM moments resulting in lower exchange bias.