A single-crystal compensated ferrimagnet Ni4Nb2O9, consisting of two antiferromagnetically coupled ferromagnetic (FM) Ni2+ layers with opposite moments in the ab plane, exhibiting non-interface exchange bias (EB), was investigated. The magnetization hysteresis loops M(), measured at a weak field H rotating in FM layers clockwise and then counterclockwise, show two successive M flips in opposite directions with a large hysteresis of the flip angle MR. It was found that the angle MR shifts due to EB to the higher or lower values, depending on the sign of the unidirectional anisotropy EB specified by the field cooling protocol. Furthermore, the EB effect also influences the temperature of spontaneous switching Tsw from negative to positive magnetization, which occurs below Tcomp = 33K, at a constant field H. Namely, Tsw decreases in the presence of positive unidirectional anisotropy and increases in the presence of negative anisotropy, indicating that the energy required to flip M depends on the sign of EB. The new features discovered allow us to more fully comprehend the nature of the EB effect in coupled FM layers of compensated Ni4Nb2O9 ferrimagnet.