Glacial/interglacial dynamics during the Quaternary were suggested to be mainly driven by obliquity (41-kyr periodicity), including irregularities during the last 1 Myr that resulted in on average 100-kyr cycles. Here, we investigate this so-called Mid-Pleistocene Transition via model-based deconvolution of benthic δ18O, redefining interglacials by lack of substantial northern hemispheric land ice outside of Greenland. We find that in 67%, 88% and 52% of the obliquity cycles during the early, middle and late Quaternary, respectively, a glacial termination is realized leading to irregular appearances of new interglacials during various parts of the last 2.6 Myr. This finding suggests that the proposed idea of terminations leading to new interglacials in the Quaternary as obliquity driven with growing influence of land ice volume on the timing of deglaciations during the last 1 Myr might be too simple. Alternatively, the land ice-based definition of interglacials needs revision if applied to the entire Quaternary.